male rex rat

Question
I have 3 male rex rats, all that I bought two weeks ago. Already I took them to the vet fpr an upper resp infection. The vet  prescribed. Them amoxicillin for1 0 days . My one male lost all hos hair completely and his skin has a blueish black tint to it which seems like bruising butthere are no songs of bullying at all by hos brothers o don't know if that's just his skin tone but it seemed to come out of nowhere and his brother's are all pink skin toned .

Answer
It sounds like you have a double Rex. Double Rex rats go through several molts during their lifetime, where they lose much or patches if their fur. Darker colored double Rex and hairless rats have darker skin- almost a blackish-blue color. So if your Rex rat was black and now has lost the hair, the skin will be this darkish color. I would assume your other Rex rats must be lighter in color if their skin is pink?