My vagina stings badly and feels swollen after sex, but only after my partner ejaculates inside. why is this?

Swelling: It could be an infection or STD and is more likely if this is something new for you. I'm assuming that this is unprotected sex, but if not some women have reactions to spermicide on the condom or to lasix (furosemide). Women can also form antibodies to sperm, but the effect is usually on the sperm, not the vagina. If could also be an allergic reaction if you're using a lube, especially if oil based lube

Allergy: You are likely having a local allergic reaction to the plasma of the semen. This can be just local or systemic, and it sounds like yours is local. You can try using preventive antihistamines prior to intercourse, or use condoms. If this this not satisfactory, then you will need to seek immunotherapy as a solution.