Hi, I have had a baby that had breathing problems and feeding problems, so I don't like to make light of anything like this. But on the other hand I don't want to completely freak you out either if there isn't an issue.
So here is my advice. But first a couple questions. When he does the gasping thing is it while sucking or is he coming off when he gasps? Do you notice any other signs of distress like red, watery eyes? Does he spit up a lot?
First of all, I definitely think you should feed him in front of your pediatrician. It is hard for them to distinguish what is normal baby noises and problems if they are not hearing them for themselves. It could easily be that he is getting too much milk and just gasping because it is going down too fast. If that is the problem you may need to check his nipple size and make sure you are using a slow flow nipple. My babies have always been breastfed at the beginning, but I know that those first few weeks when the milk supply is so high, they do a lot of gasping, but they adjust eventually.
I was thinking that a lactation consultant would be helpful, but since you are not breastfeeding, I'm not sure if that would work. But they are good at telling if there is a problem with the baby that needs attention. If you have access to a speech therapist they can tell the same things.
Oh, one other simple thing to check is if his nose is stuffed up. Babies have trouble eating if their nose is congested. You probably have already checked this and since it is every feeding that is probably not it, but if it is a problem you can put saline solution in his nose to soften it up and then suction it out with an aspirator.
Well, hopefully it is nothing, and he will adjust in time. But don't hesitate to keep pursuing help if you think there is a problem.