Babies can make a lot of noise while stuffy but not be getting a lot of milk. In my non-medical opinion I think you need to get him un-stuffy. Also, too much aspirating can irritate the mucus lining and make it swell, causing more congestion.
At six months I would think it would be okay to supplement with a bit of water for this situation. You could take a syringe and give him ~ 1/4 tsp every 15 minutes, maybe a bit more. When my kids are sick with vomiting if I give them a Tbsp every 15 minutes they stay well hydrated, and they're 5 and 3.
You might also make a bit of tea, I would give mullein tea made from the leaves to my daughter when she was little (~2-3 months starting out) to help her clear her lungs. The mullein helps a person produce mucus so they can finally cough it up. It can also calm a cough.
Kali bicromicum is also useful for those nasally colds.