This a very good—and common—question. The short answer is yes, but it’s very unlikely.
A small percentage of women (about 1 percent) are allergic to the enzymes in their partner’s ejaculate. Symptoms of a true semen allergy include redness, burning, and swelling where the semen has come in contact with the skin. Hives and difficulty breathing are incredibly rare occurrences but require immediate medical attention. It is possible to perform testing to see if what you are experiencing is a true allergy. If you are found to have an allergy to your partner's ejaculate, condoms can be used to minimize contact. There is also a treatment modality, done by an allergy specialist, to desensitize you to your partner’s semen. If you are trying to conceive, and you decide not to proceed with desensitization, assisted reproductive technology may be used.
Most often, discomfort after intercourse is the result of something else. Since the pH of your boyfriend’s ejaculate is different from the pH of your vaginal flora, the combination can cause your vagina to become irritated and inflamed. While uncomfortable, this situation is not dangerous and will resolve without intervention in a couple of days. You can minimize the risk of pH shifts post intercourse with condom use. Another cause of vaginal discomfort after intercourse is simply friction. Maintaining excellent lubrication during sex or using lubricated condoms can help minimize discomfort. We recommend using an over-the-counter water based lubricant.
A bacterial or yeast infection could also cause vaginal discomfort after sex, but these would likely be accompanied by an odor and/or unusual discharge. Infections need to be treated, so if this is the case, be sure to call your doctor. Lastly, women can have a sensitivity or allergy to the latex in condoms. If this is the case, my recommendation is to see an allergist about a potential latex allergy and switch to lambskin condoms, but talk to your OB/GYN first because these types of condoms do not protect against sexually transmitted diseases.