Here, I just copied/pasted my response in your other post that turned into a cluster, lol. If you could just answer the questions about your husbandry as closely as possible we can make sure everything is okay and help you where you need help. Again, I think your dragon is just doing normal mouth-gaping to regulate body temperature while basking, but if he starts exhibiting any of the symptoms I listed, like wheezing, coughing, clicking, or excess mucousy strings around his mouth, then he need to see a Reptile Vet to have a culture taken to check for a bacterial or fungal infection.
Okay, wow, lot of stuff going on here, lol...
Back to the OP with the original problem, so for the past 2 weeks your juvenile has been puffing his beard up and opening his mouth...They do this for a number of reasons, it does not sound like a respiratory infection, usually with a URI they wheeze, cough, make clicking sounds when they breath, and they have a lot of excess mucous around their mouth when they open it, in strings.
This sounds like a husbandry issue, probably with your temperature zones or your lighting. I did notice that you have 2 compact lights on 2 different sides of the tank. This represenst a problem in and of itself, because you should have a bright-white colored basking bulb (which is the correct wattage to put both the Basking Spot Surface Temperature and the Hot Side Ambient/Air Temperature within the correct ranges) and a
UVB light BOTH OVER THE HOT SIDE OF THE TANK, RIGHT ALONGSIDE EACH OTHER, WITH HIS BASKING SPOT/PLATFORM DIRECTLY UNDERNEATH BOTH LIGHTS! This is how you achieve the goal of replicating natural sunlight for him, so he gets both lights at the same time while basking. So that's problem #1...(Unless you are using a Mercury Vapor Bulb)...
Usually when they open their mouths inside their tanks like that it is because they are trying to regulate their body temperatures. It doesn't mean that they are too hot necessarily, it could, but it can also be completely normal. But we need to know some things about your lighting and temperature zones:
#1.) What type of thermometer are you using to measure the temps inside his tank?
#2.) What are the CURRENT temperature readings of his Cool Side Ambient/Air Temp, his Hot Side Ambient/Air Temp, and then his Basking Spot Surface Temp?
#3) EXACTLY what
UVB light do you have for him (Brand, Wattage or Strength, and what type is it, meaning is it a compact, a coil, a long, fluorescent tube, or an MVB)?
#4.) Is the
UVB light on top of a mesh lid to the tank/ How far away, in inches, is the
UVB light from his Basking Spot/Platform? How many hours every day are you leaving both his
UVB light and his Basking Bulb on?
#5.) What wattage and color of Basking Bulb are you using? Is it a regular, halogen basking bulb/Indoor Flood Bulb, or is it coiled/spiral?
#6.) What is his normal daily diet? And how many days a week is he getting a calcium supplement and a multivitamin supplement?
You're using a solid substrate, so that's good, often times they get chronic Upper Respiratory Infections when they are living in ANY TYPE of loose substrate, as all loose substrates are breeding grounds for all types of bacteria, fungi, parasites, etc. and they harbor these microbes from the moment you put them in the tank, no matter how many times you change them or scoop out dirty substrate. Most people think of bowel impactions being the #1 issue with loose substrates like sands, crushed walnut shells, bark, wood chips, rodent bedding, etc., and this is a huge issue, especially with babies and juveniles under a year old, but Bearded Dragons are VERY prone to Upper Respiratory Infections, Eye Infections, and Skin/Scale infections, so loose substrates are just an unnecessary risk that owners take, and I can't for the life of me figure out why, because they are not at all natural for a Dragon, they come from the Australian Deserts, which have little to no sand at all, they are a hard, rocky terrain, so you're forcing them to live in an unnatural environment, and then on top of that you are risking all of these serious health issues every day, all day long, simply because you like the way it looks I guess...disposable paper towels would be better...
Anyway, that's not your problem, and I don't think it's a URI, though it could be, but we'll know a lot more once you answer the above questions as closely as you can. You can find the info right on your lights if you don't still have the boxes or don't remember.