It is possible that people can be allergic to latex from the condom, the protein in the semen or conten in the lubricant.
All can cause real discomfort and you should look for condom that are non-latex based and lubricant don't have things that one is allergic to to overcome this issue. Some people are allergic to oil based lubricant but not to water based. Make sure you read the ingredient label carefully. Example, if you are allergic to nuts and the lubricant has Macademia nut oil based or some flavor based lubricant then it can cause a reaction.
News Article -
http://abcnews.go.com/Health/AllergyAndAsthmaResourceCenter/story?id=1799906&page=1
Kissing your partner can also be dangerous for folks with allergies to foods. There is instance where a kiss from a boyfriend who ate peanuts hours ago lead to death for the girlfriend.
News Article -
Nut allergy: With one kiss, I could kill my husband - Telegraph
Update: After further review of the the "Death by kissing" news article, it was brought to our attention that the previous information of the death by kissing in Canada was not due to peanut allergy but due to Asthma attack that the girl had.
News Article -
Quebec teen died of asthma, not nutty kiss
Regardless, have yourself tested for allergies to find out which substance you are allergic to. Once you have the doctor do the test then you can use those results to weed out the things that causes an allergic reaction. Even the smallest traces of allergic substance can create havoc on your body.
Good luck and happy love life.