Wow, I don't know anyone who has allergies to leather. Do you have other types of allergies? If it's truly a contact allergy, I'm afraid you have to avoid getting in contact with your leather bags. I'd see an allergist.
Well in the beginning, I didn't know for sure and I thought it's was something I had eaten. That time I was carrying a caviar bag, medallion shoulder type, so my palms, arms And near armpits, those areas that my bag touches them. Because I only uses my leather bags during weekends if I m going to the city, therefore normal day I used my nylon Kipling. After several occasions, I realized it was the leather that gives me the rashes. It just comes.I don't see how you can tell for sure it's the leather of the bag causing this. In high heat, maybe anything pressing or rubbing your skin would cause the same reactions. Worth trying it out with other materials to check this--try a cotton or woven fiber or nylon bag with the same weight as your leather bags. Carry it on the shoulder and by hand, and see what happens. Perhaps you're just allergic right now, to something in the environment?
Yes, as Mariapia said, it might be the chrome. Chromium-tanned leather is common.
See an allergist to have tests done. In the meantime, use an ascorbic acid (vitamin C) barrier cream.
If you have any bags that you know are vegetable-tanned, maybe try wearing those for awhile to see if your skin reacts to those too.