Most likely. Probably need a vet appointment for a respiratory infection. The way to stop it from getting worse and maybe it'll help you get rid of it is to make sure his temperatures (everywhere in his enclosure) is 85 and above at all times. Even in the corners and inside any hides. When he's not sick anymore you can reduce the heat to 80. They should have a basking spot and one corner of 100 degrees. Best way to measure these is using a digital thermometer / hygrometer or a temp gun. Not the button type stick on dials. I use the one pictured.
Babies need humidity to grow smoothly and retain hydration. However adding humidity when you don't have the temperature up will make him sicker so don't bother until you got him healthy and are sure of your temperatures everywhere in the enclosure. It will be next to impossible to maintain heat and humidity in an open-top enclosure so you may need to switch him to a closed-top enclosure or enclose the enclosure that you have.
I would soak them in warm water in the morning so it warms them up and gets them ready for the day and really anytime is nice and warm outside for them, every bit of sunlight helps them. Just be sure to keep a close eye in them because a baby tortoise is a good meal to a lot of other critters.
Unless the temp is 85 or higher I wouldn't sun bathe the sick one. In your picture the smaller of the two that has his arms and legs pushed out seems a little scrawny. It may be that it needs to be hydrated more often. Young ones need warm bath sometimes twice a day. With your lights in middle of enclosure it may be too hot. Do they have a spot that's only 85 where they can cool down? How are you measuring temps? I would hate to hear they died from overheating.
the young one named Day
Day has a cold
Day has been sleeping with his arm pushed out from the day he arrive
i don't really measure it
the seller tell me to measure it with my hand "if i feel warm then it is enough" that was what he said to me.
That seller is an idiot. Test it with your hand?! OMG...$12 or $13 to get the thermometer/hygrometer I attached above. You can get them at home Depot too, I THINK. I prefer the probes on wire because mechanism is outside of enclosure so not exposed to humidity. You REALLY need to measure temps. How do you know you aren't baking the poor guys? Or keeping them too cold?
No need to panic friend, you're doing just fine. It can all be quiet overwhelming at first but once you get a good routine down, it'll be very easy to maintain
You can get an aluminum dome for your lights that will force the light and heat downward towards your torts. Something like this..
What kind of UV bulb did you get? Coiled bulbs tend to hurt the tortoise's eyes. A strip bulb or a mercury vapor bulb (puts out heat and uv light at the same time) is best.
You could also get a ceramic heat emitter that puts off heat with no light, these are great for keeping your babies warm at night.
When I first bought my baby Sulcata, just about everything I initially acquired was wrong and the folks on this forum helped me and now my Sulcata is healthy and growing just like he should be
The height of that lamp worries me. Can you put your hand on that stone and leave it for any length of time or does it burn you? Raise it a bit if it burns you. I would be a wreck without a thermometer...