Welcome to our forums and congrats on your new little friend!
If you could show us a picture of him, we might be able to take a guess, as well as make sure it really is an Irian Jaya.
THIS is a thread showing you how to upload photos.
If your BTS is only a month and a half then there's a very high likelihood it is a baby born to a newly imported, wild caught female --just judging by the time of year he was born; it may be a good idea to have an exotic vet do a fecal test on him to check for parasites. Just a precaution I would personally take.
You may also want to have a read-through
HERE --it's a collection of easy links I've put together to some reading that'll give you a good grasp on the basics. I think you should especially check out the food chart and start feeding him some better protein, like some wet dog food.
Your basking spot sounds a little bit too low, but I'm reluctant to have you raise the temps too much in a small 10 gallon tank as that may make your cool side too warm for him; just keep it in mind when you move him into a bigger tank. If he really is an Irian Jaya, with the night time temps getting that low, I'd worry about inducing brumation for him, and in my opinion, if he is that young, that might make it harder to get some good weight on him during his biggest growing period. You may want to think about supplying some nighttime heat for him, like a red- or a moonlight globe, an under-tank heater, or a ceramic heat emitter --although, you'd have to put a dimmer on a CHE if you're using it on a tank that small.
OK. Now to your breathing question.
It can be nerve-wracking in the beginning before you know what "normal" looks like, but from your description it sounds OK....
HERE and
HERE are two (long and boring

) videos I shot just to show how different and seemingly erratic their breathing can be. I hope these help.

(On the first video, you can see some of that breathing movement between the front legs and the jaw on the third skink; I know it's maybe not as much as what you're seeing, but it's quite normal for them to breathe that way.)
If you do take him in for a fecal test, the vet will listen to his lungs as well, and that might make you feel more at ease too.
Keep us updated on how things are going for you.
....and get showing us some pictures..... we LOVE pictures!

Breeder and keeper of Meraukes from 2010 to 2022.