Alright, you've got a lot of husbandry issues that you need to get corrected immediately or she's not going to make it. First and foremost you need to get all of the sand out of the enclosure immediately, completely disinfect the enclosure and everything in it inside and out (all decor, bowls, basking platforms, etc.), and once it's all disinfected with either F10SC disinfectant or bleach and then rinsed well and completely dry, you need to put down clean, dry papertowels on the bottom as her only substrate, and just throw them away and replace them as they get soiled. Bearded dragons should not ever be on ANY loose substrates, but particularly babies and juveniles should not ever be on any type of sand, crushed walnut shells, bark, mulch, wood chips, rodent bedding, gravel, pebbles, rocks, etc., nothing loose ever. They are all a huge impaction risk, especially for such a young baby, and they also harbor lots of bacteria, fungi, and parasites, and will just keep reinfecting her until removed. Plus, the sand is no doubt getting in her eyes and is probably one of the main contributes to her conjunctivitis. So please do that now, and after cleaning put the paper towels down. You can worry about a permanent solid substrate like ceramic or vinyl floor tiles, Non-adhesive shelf life, etc. later, for now just get that sand out, get it completely disinfected, and get the paper towels down.
You're lighting is completely inadequate for a bearded dragon, and her lethargy, eye-shutting, any appetite loss, etc. that is already happening (or no doubt will happen soon) is due to inadequate UVB and UVA light for a bearded dragon, along with inadequate temperatures, as there's no way a 50 watt basking bulb will get an enclosure that size up to the correct temperatures. And why do you have the basking light on with the UVB tube off? A 5 watt UVB tube is essentially doing nothing for her anyway, but you should have both her basking bulb and her UVB tube on together, right alongside side each other so she gets both at the same time while basking, and both alongside each other and directly over top of her main basking spot for at least 13-14 hours every single day! She is going to stop growing, stop eating, and develop Calcium deficiency and severe MBD without the correct
UVB light on for at least 14 hours a day. And she cannot digest her food with inadequate temperatures, and definitely cannot digest mealworms and will become impacted from them.