Should I tell him?

My boyfriend gets kinda jealous( not overly at all) and there’s a guy in one of my classes who told me he has feelings for me WHILE he KNOWS I am in a happy relationship (calling me so beautiful and all that bullshit). At night he says “goodnight beautiful”. Should I tell me boyfriend he is still advancing on me or save him the unnecessary stress?

Edit: so far people are saying I should block the guy but we are also good friends and he has some issues with his mental health and I don’t want to back out if he needs support. He’s easily triggered