Hey there! So this is kind of a tough thing to tackle.... But!
When binding, it always depends on chest size. If you're blessed with smaller breasts, you might be able to do a camisole bind. Meaning you have something like a camisole that's really tight on you (not uncomfortable but snug) and fold the bottom up to help bind, then put a shirt over it.
That's the hands down cheapest way i can think of. If you haven't heard of it before, i'm saying it here: Do not use ace bandages. They can damage you and they're really uncomfortable at that. Whatever you use to try and bind should leave you enough room to breathe, and should never constrict.
When you do have a few dollars, try ebay. There's a few companies in china and thailand that sell very cheap binders. Like.. $6-7 cheap. (Edit: Forgot to mention that some of the ebay binders look just like regular tanktops!) But until then, try the cami thing or baggy t-shirts. In the winter, layers are your friends. Shirts, sweatshirts on top, etc. Hoodies, too.
All this being said, sports bras really help too, though i know you said you don't have any. If you get them, get at least two. One to put on normal, and one to put on top of that, but backwards.
I hope i've helped! :3
