I've only had him three days now, so I'm probably paranoid, but I want to be sure he's okay. I noticed yesterday that he kept swallowing every so often, and make some sort of clicking noise at one point. Today he keeps making that clicking noise like, once every five minutes, and it's freaking me out. He is also swallowing a whole lot more than yesterday. There is nothing physically wrong with him that I can see, besides his shedding. Also, he only ate 4 crickets total yesterday, and only one during his morning feeding today. The first day he ate fine, and gobbled everything in sight, even ate veggies! I don't know what to do, I don't have money to take him to a vet right now.
Does he have thicker than usual or more than usual mucous in his mouth? The clicking sound on it's own may not be an issue. If you see thick mucous or see him appear to cough it could be a respiratory problem but otherwise he's probably OK. His appetite may be down due to the shed so I wouldn't worry too much about that as long as it picks back up when the shed is done. Try dropping a little water on his nose and see if he licks it up. Not a big deal if he doesn't but it may be good to offer some extra hydration while he isn't eating much in case he wants it.
I wouldn't force it. Wait until he opens it while basking or while eating and see if you can get a look. If they cough they tend to open their mouths frequently. Here is an example. Dundee's mouth is open and is swollen but you can see that he has strings of thick mucous along the sides and inside his mouth. If you aren't seeing that, then that's a good sign.