Today I talked with the vet, for now the tail is not infected, I will apply some special cream in the tail 4 times + peroxide in the tail 4 times + special antiobiotic they gave to me 2 times day.
Going to vet is always a great idea, it gave me hope, sorry for my bad english
note: if you apply some cream on the animal be careful if the rat eats or lick it it can be toxic, vet gave me a honney based cream
Sorry for my bad english, thank you for your intherest <3