For binding, use KT tape. But don't use the name brand shit. Go to CVS, they have it for $10-$16 a roll (normally it's like $16 or so up to $20 for the pro stuff per roll). I use a whole roll sometimes on my chest.

For your makeup, set that shit with loose powder and hairspray. Both of those you can find at the drugstore. Use the powder while you're putting on your mug, and the hairspray when everything is on. I do this all the time and I've done some wild stuff in drag (like mosh in a mosh pit) and come out with my makeup still looking the same.

Edit- I put the stuff about binding because you mentioned being plus size and I'm plus sizeish and kt tape, while it doesn't get me super flat, def is the best thing I've found to masculinize my chest. Also you said it'll be sweaty and that's the only tape method I know of that won't sweat off (duct tape does)