If you leave the two mattresses, yes, you'll eventually fall down the middle. You should tie them together with rope or twine, then get a queen or whatever size mattress to fit.
If they are extra-long twins, then pushing them together will make a standard king size bed. You could buy a fitted set of sheets for king size beds.
You can make a bolsters by rolling blankets as thick as you needed, in the middle of the mattresses, and cover all with a fitted sheet, and the rest.
Or buy a king mattress to sit on the two box springs
I share a twin room with my sister but she's moving out, if I push the two beds together will I just end up falling down the middle or does it actually work as a double?