Asthma? Kinda long btw

Okay ladies I really need opinions on if I'm just over reacting or if I should be worried. 
So first things first my son is 14 months old. He was born 5 weeks early and was in nicu for 13 days. The first day he was in nicu they had him hooked up to everything around the beginning of his second day they took him off of the cpap and ocygen and pretty much left everything else for a little longer. Well around 5 months he started learning to crawl and started doing a weird breathing thing in the afternoons before bed. I always thought it was from him fighting sleep (he only did it once every few days when he fought sleep) so I didn't get to worried and it ended up going away well now he's figuring out how to run and he's a lot more active. But he will get really worked up and start coughing. Then if he keeps playing as hard as he is he will start acting like he's really short of breath and his cheeks will turn red. 
There are some people on my dads side of the family who have asthma. So should I get him checked for asthma or is this normal in a baby his age?? 
**photo just for attention**