Deffinitely increase the temps to 115F with cooler areas available on the basking sight. It's good to have a range of basking temps so your dragon can move to whatever temp is ideal for it. They always seem to for the hottest spot first thing in the morning and right after eating.
When you say your dragon is only three inches, is that head to tail tip? or Head to vent length? Bearded dragons tend to be 3-4" long head to tail tip straight out of the egg and if yours is only 3" from nose to tail tip, then it must have been a real runt out of the egg or a Rankin's Bearded dragon (which are smaller than the common bearded dragons, Inland Bearded Dragons). With a dragon this small, you need to mist it 2-3 times a day to ensure it doesn't dehydrate, soaking is useful as well, just make sure the water isn't any higher than the dragon's 'armpits'. A stone or rolled up clean washcloth in the water gives them something to hang onto so they do not become tired and risk drowning.
I would not feed mealworms at all, especially to such a small dragon. Mealworms are noctoriously hard to digest, especailly for baby dragons. Their exoskeleton is very tough and can cause impactions. Instead feed 1/8th to 1/4" crickets (often called 'pinheads') no bigger than the space between the dragon's eyes. These should be dusted once daily with a multivitamin and calcium D3 powder. A pinch of each in a ziplock or other small bag, then add crickets and shake till the crickets are lightly dusted. Then feed immediately to your dragon. Make sure the crickets and other insect foods are well gutloaded 24 hrs before you feed them to your dragon, this ensures they are full of good nutrients etc. Gutloads for crickets can be commercially bought, or better yet, provided by yourself. Best foods to feed crickets, is the same assortment of wholesome greens and vegetables fed to dragons (collard greens, dandelion greens etc). A slice of orange, potato, carrot or squash can be giving to teh crickets as a moisture source.
Bearded dragon babies should be fed 2-3 times a day, all they can eat in a 5-10 minute period.
You mentioned you are not sure if your dragon is pooping? You should see fresh poop in the cage at least daily. All poop should be cleaned out daily as well, with papertowel (newspaper etc) changed daily to keep your dragon as clean as possible. It wouldn't hurt to take a fresh poop sample to a qualified reptile vet (in this case, any vet can do, but best to find one experienced with reptiles) for a fecal, to test for internal parasites.
Finally, since you only had him for a couple weeks, there still is a possibility he is still adjusting to his new home.
Another thing you can try is give him a bit of diluted gateraid, to help encourage him to drink and rehydrate him and replace any lost electrolites, if he is in fact not eating well. It could also help stimulate appetite.
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PHLdyPayne