little cough

My prem is 4 months old and the last week he's had a bit of a cough. I don't think he's ill, in fact I'm not sure I could even call it a cough as it only happens every few hours and it's just a few dry coughs almost like he's clearing his airways or something.

He's probably sneezed every day since he was born, but I'm finding he's started sneezing a few times a day too. I'm wondering if he could have hay fever?! is it possible in a tiny baby (he's 7lb)

Or should I get him checked out? he's fine in himself, content, feeding ok etc.

I have to use the nasal aspirator (maybe twice a week) because he gets a blocked nose a lot, and sounds bunged up when he cries.

Sorry first time mum to a prem so I sort about everything.