A picture would help. Might be contact dermatitis or a latex allergy. Eczema usually has an itch component. Believe me I know!!

Mine just split open on the fingers but only in the wintertime because my hands get so dry. It hurts like heck. Never really heals all winter long.

Make sure it's not a fungal infection. Go to the Derm

I had a bad case of exzema, the pharmacist said to use rubber gloves cause at the time I was giving my husband nebulizer treatments and used a lot of hot water. Now I am exzema free. Not long ago I had it on the heel of my foot. I bought otc exzema treatments. My doctor said to mix the otc with the generic of cortisone and I did but my heel didn't heal for months

Is it possible you have eczema? I have this on my hands, cracking/bleeding and burning is definitely the sensation I feel, if I put on lotion it stings. I get this from the cold and dryness or a lot of washing. I happened to have a sample if aveno baby eczema cream and I tried it on a lark and it helped A LOT. Might be worth a try, good luck ❤️