Yes, it is possible. Some women (not many) can have an allergic reaction to proteins in their partner's semen. Symptoms of semen allergy include redness, swelling, burning, and itching at the contact site (usually the external genitalia). In more severe cases, systemic allergic reactions such as hives, itching, and difficulty breathing can occur.
If you are highly sensitive to semen, using condoms is one of the most effective ways to prevent an allergic reaction. If you wish to become pregnant, artificial insemination (with the semen proteins removed to prevent an allergic reaction) or in vitro fertilization are viable options.