I do not like to guess when it comes to chest pain. I would suggest he see his doctor or the ER as soon as possible. It could be nothing and given the fact he does not have any other cardiac related symptoms, I would suspect this to be the case, but still, it is better to be safe than sorry.
One question, do you live in a dry climate? Sometimes dust and low humidity can cause a tightness, the reason I ask is because you said in the rain, he felt better, humidity sometimes helps folks, it does me if it is not too high.
Anyway, I would get this looked into, just for peace of mind if not for anything else.
Ditto the above poster. Take him to the ER or squeeze-in emergency appointment with regular doc today, whether your fiance likes it or not. But probably had him a little wheeze until the rain came.