"You're wearing your t-shirt inside out" – Correct. "You *have* your t-shirt on inside out" – Correct. "Your t-shirt is on inside out" – Correct. "Your t-shirt is inside out." – Correct. The difference between these last two is only that in the first sentence, the "on" means that the listener is wearing the shirt. So in this case, the listener is definitely wearing the shirt. You might say the second sentence when the listener wasn't wearing the shirt. For example if it was folded inside-out. But more commonly you could also say it if the listener was wearing the shirt.

To "have" your shirt "on" is a phrasal verb, meaning to "wear" your shirt. If we actually say to "wear", then we don't use the word "on" (as it is not used as part of a phrasal verb with the verb to "wear"). When we use to "be on" in reference to your shirt, that is another phrasal ver similar to to "have... on".

A small correction: "You're wearing your T-shirt on inside out." sounds a little strange, but "You have got your T-shirt on inside out." is common. "You're wearing your T-shirt inside out." is perfect. Good luck!