This is a little late but have you thought about trans tape? You can tape your chest down- I've done it a few times, but there's plenty of videos online about how to safely bind using TRANS tape. Do not use bandages or duct tape or anything, make sure its trans tape (kinesiology tape is also safe, it's essentially the same thing and drug stores carry it often). There's not as much compression as a binder, but it still helps imo.
Now, about free binders. Don't go in blind- Most binder companies have a size chart. Make sure to take your measurments and see what size you are. If you've been doing that and it still hasn't fit, size up. Obviously thats not always possible with limited sizing options, but thought I'd say so just in case. All that said, here's a link to a post on tumblr about where to get free binders. Some of the wait times are long, but there's a few different options. Hope you find something that works!
https://www.tumblr.com/the-maddened-hatter/733173178422149120/hey-so-yall-are-1000-fine-to-reblog-this-but-i?source=share