Pink/ Red Eye, Itchiness, Sore, Puffy, Etc After I Had Sex

Could be conjunctivitis and might be coincidental but is often contagious...

Probably caused by irritation from a foriegn body which might or might not still be present - such things can be caused by momentary contact with flying insects, your hair, his hair, dust or grit, etc.
It is possible your partner managed to poke you in the eye with something more substantial (such as a finger) while you were so occupied you didn't notice...

The frantic activity of sex might have caused a minor blood vessel in the eye to rupture and turn the white into pink but the degree of irritation is usually small and it doesn't usually cause swelling.

Suggest you visit your local A&E department as they are better equipped to deal with eye emergencies than doctor's surgeries or pharmacies. If it does turn out to be only a burst blood vessel it would be worth getting tested for diabetes - one of the many possible symptoms is thinning of the walls of blood vessels in the eyes...

It's possible, he has long hair, but I poked him in the eye with my finger by accident, not the other way around. My eye is just a little bit irritated now (some redness) and the swelling has gone down.