It starts off with a professor who meets a guy in the park and they hit it off. Later on (maybe it was different characters at this point) one of the guy's was going to medical school in the u.s. and was depressed that his lover didn't contact him. He later came back to the lover's apartment and they became a couple.

It sounds like the beginning of the story revolving around the second couple ("Junjou Egoist") from Junjou Romantica.

Totally Agree.