I also get sick and tired feeling after a shower and I have to lay down for a while after I get out. I don't know if it's because of my autism or maybe it's subconscious sensory problems or something else
This depends a bit on the kind of “sick”. If it’s the lethargic, “I think I might have a cold” kind of sick, it’s probably the sudden drop in temperature and you should try to keep yourself warm as you dry off, and then get under some blankets until it wears off. If it’s dizzy-sick, this could be a problem of your inner ear being drawn out by the heat, the humidity, or the water; talk to your doctor in case it’s treatable, but it might just be how things are, and being horizontal or at least well-supported for a while is a good idea. If it’s “I just ate bad food” sort of nausea, though, hot water shouldn’t be doing that. If you’re eating or drinking something in or just before your shower, stop that for a little and see if it helps. Otherwise, you *need* talk to your doctor in as much detail as you can. That sort of problem with heat or moisture means you’re at some risk of suddenly passing out, and you need professional help. They might not be able to fix it entirely, but they can often make it better and stop you hitting your head on the bathroom floor.
As far as whether it’s autism: There’s not enough information to say, really. Autism can affect the “unconscious” senses and how we process them as well as the more well-known ones, certainly. But so can a whole range of other things, and some of them will deteriorate without treatment.