Unity isn't very accessible. It can be used to make audio games, if you can get sighted assistance. The thing with most tools like scripting language compilers that aren't accessible, is that most of the time, typing the code into a file isn't the problem. The problem is the compiler most of the time. BGT is complex enough, depending on what you want to do. So, you might try to show your teacher a game made in BGT and give some background info on it.

Are we talking about making 3D objects do 3D things?
In that case, BGT is not going to be all that great (I made a 3D library for BGT, but I am not an expert at 3D things and it is very minimalist).
Python with pygame/pyglet, with Pyode/Panda3D/Bullet might be better for complexity's sake.
I looked into the 3D packages available for Python over the summer, and my conclusions were:

• VPython is amazingly simple (but only does graphics, no physics, and I couldn't get my tests to actually work)

• Pyode beats Bullet and Panda in terms of learning curve and speed.

• Panda is portrayed as a complete 3D game development platform that is supposed to be fairly easy to use. The tutorial drove me crazy very early on, but that might just be me.

• Visualpyode / VPyode combines Pyode with VPython to get graphics and physics all in one package. While it's still pretty high-level, some nice features of the two packages get lost for lack of analogues (I think there are work-arounds for these, but they were kinda cumbersome to hunt down), and the object hierarchy gets more complicated (not Java3D complicated, thank the light). It was also a pest to hunt down because of poorly labeled links and the fact that Source Forge.

• There are others, but you would have to pay me to try and mess with anything that low-level when the above packages exist. My brain is complaining vigorously when I tell it to go work on a simple UTF8 program; shaders and rotation interpolaters and combining multiple vectors and scene graphs in which half the parts don't actually do anything and are just there for somantic reasons... I'll take VPyode, thanks.

So.
I'm assuming this is some sort of game programming class or something for high school as opposed to college.  If it is a game programming class and it is optional, I'd get out if possible: so much of it is going to be visual, up to and including making/getting/working with graphical resources; your time would be better spent online or in a more general programming class.
That said, BGT is probably not going to work.  This is not about complexity-ironically, BGT is probably more complex than unity, at least if you're trying to do the same things that unity does.  A lot of the draw of unity is that you can literally edit the game while playing it, or at least seeing how it will look to a player: it gives you what is basically visual studio on steroids, and you build really, really complex maps by using what is basically paint on steroids.  "When the player is this close to this object" is all drag/drop/click the menus, and then "execute this script" is finally, at long last, coding.  Walking is handled.  Collision is handled.  Physics?  Handled again.  At least half of unity is about the artist, not the programmer, and consequently Unity lets the artist do a lot of what people think programmers do.
So basically, without any programming at all, you get a truly tremendous amount of stuff.  Epic.  Give me something equivalent for audiogames, and I can give you a new audiogame literally as fast as I can figure out level design.
BGT does nothing like this.  BGT doesn't even have graphics, not unless something happened while I wasn't looking.  The ability of your teacher to grade or even appreciate a project done in BGT is limited, possibly nonexistent.  If you wanted to duplicate unity in BGT, assuming someone gave you graphics, you'd be looking at 5-10 man-years, linear algebra, trigonometry, possibly basic calculus.  Most of the systems for the sighted are this way.
There are literally two alternate universes here.  The universe of blind gamers is so far from the universe of what Unity does that, unless you've played a game for the sighted, you are probably not able to appreciate the differences.
If you have a sighted partner, looking at one of the code-based engines will do the trick, but you won't be able to go nearly as fast as your sighted peers because you'll be implementing stuff they get for free: as an example, collision detection, a scripting system, etc.  The stuff you have to deal with to make a Unity-level game without Unity includes all the aforementioned maths (yes, even if you have libraries.  Understanding those libraries requires it).  There is no accessible alternative: even things like Panda3D don't come close in the sense that they're still slower, at least not for a blind person-any of these frameworks may have comparable tools, but the tools have the same exact challenge as Unity.  I surveyed all of the RAD options for games for the sighted, especially MMO-style games.  They are all basically Unity by another name, and most of them don't even have accessible text editing.
All alternatives in this thread are like comparing spaceships and the internet.  Both are very technological, great examples of their type, wow humans have come a long way.  But the internet and spaceships have nothing in common.  The world of Unity and alternatives to Unity is completely separate from the world of <3 or 4 packages and purely programming>, in much the same way that these don't even compare.
Sorry to be the bearer of bad news, but there is no purely programming approach that is even comparable.  No matter what you do, you're basically going to need a different syllabus or to work in a team and take the back seat on everything.  To do the same as your classmates, you will have to deal with at least 10 times the complexity and probably 100 times the code.  The games you will make due to your visual impairment will not be able to incorporate the third dimension, at least not with the time you have (I'm assuming the standard semester).  Even if you had more, literally the only example that comes close is Audioquake.
As for making graphical games as a blind person in general?  Not without sighted help or remaining vision.  CAE is the only one who is trying to my knowledge, and I don't think he's managed it yet.  I also think he's having help (CAE, correct me on this if you've somehow managed to do it without).

Hi, thanks again for the advice. I'm not sure my teacher wants the game itself to be complicated, they just want to make sure I'm getting the same or similar things out of the class as everyone else. Alternatives are definitely possible, though. It doesn't even necesarily have to be a game being programmed, as the gaming part of the course is only being done in the first term. I suggested an audio game, so I could be doing a similar thing to the rest of the class.

Hi, it's in between high school and colege level, if that makes any sense. I'm taking it through high school but I also get university credits and such for completing it.

Hi, thanks again for the advice. I've seen what you mean with teachers who don't really know what they're talking about, but that doesn't seem to be the case. They just weren't sure how complicated something like this would be as audio games are something that most people haven't encountered before.