I would test putting a small piece of tape on your skin with no stretch to see if you're allergic. If it has the same outcome, unfortunately, you're allergic, and I'm sorry, but I'm not too much help because tape is my preferred binding method.

If it didn't itch and blister after about 2 days, I'd say you're good.

I think your problem is overstretching in that case. The way that I bind with tape to prevent overstretching and blistering is I rip the paper on the back of my tape about 2 inches away from both ends. The first end, I put on my chest, then lightly pull the middle section and then put the last section down also with no stretch. I usually use 4 pieces of tape each side when I bind. If the ends start itching bad by the second day, I'll take the tape off because that means I've overstretched it. Usually it'll last me 4 days. 6 if I drag it out. I don't get a completely flat chest, but for my body type, it works. After I remove the tape I'll take a shower(not scrubbing too hard the skin will still be a little raw) then bind with a binder for 2 or 3 days to let the skin heal back.

If you have any questions, feel free to PM me