That sounds really awful. I'm sorry that you're going through it.

Honestly, I don't think an air mattress on top of your bed will help much. If you're feeling vibrations coming from the floor, through the frame of the bed, through your mattress... an air mattress just doesn't seem to have the density, I'd guess, to help buffer that.

Given the situation you've described (super small space, it sounds like there's no where in the space to really get away from the vibrations) - I don't know that there's much you can do. Especially as a renter (i.e. you can't do any kind of construction).

Are the vibrations from the floor mostly? Or the walls? or above you?

I've heard of people using heavy throw rugs on the floor to help absorb some of the noise/vibration from below them. Maybe with a carpet pad underneath?

[Edit to add - I've had people suggest that using tapestries on the walls can help with sound coming from the other side.]

I don't know for sure if it would help... but some bedding materials are made so that you don't feel your partner moving around during the night. So they're made very specifically to absorb/minimize vibrations. I think latex could do this (but you might want to check online, I'm not 100% sure). If so, you could look for a bed "topper" made out of this material.

I'm just not sure it would be effective though, since it's the whole bed vibrating from below, rather than someone else, next to you, moving. But it might be worth looking into?