Yup, it took 5 years in nursing before I developed mine... I thought I was going mad for a while, oddly itchy, red hands that got better on days off, I didn't make the link, lol.
I eventually figured out what was going on and went to occupational health, they agreed with me and a letter was sent to my ED telling them if they did not supply latex free gloves, I was entitled to leave work with pay, lol... needless to say, my pretty purple latex free gloves are all over the department now
It's not that difficult to get used to... oh and don't forget that if you have a sensitivity to latex, it can quickly escalate into a full blown allergy... and that includes condoms, wouldn't like to have any embarrasing visits to your own department