u/Individual-Panic-388

Hello! I am not new to owning cats but this is my first kitty i've owned outside a family setting. My sweet boy who I just adopted is a little fur ball, we are unsure of his age but definitely within the 1-6 year range. He has medium length hair and I knew before adopting him i would have to prepare to care for his coat. When i brought him home i instantly groomed him and washed him with Earthbath hypoallergenic cat wash. When he was dry i groomed him some more and to my dismay most of the hair at the base of his tail had fallen out. I instantly started researching and i'm fairly certain it is stud tail. His tail is very greasy, has black dots and i believe the area looks irritated, maybe even rash like? He was neutered very recently and from my understanding it takes a couple weeks to subside as the body hormones adjust. The area does have a faint odor and i'm very nervous i will have to bring him in to the vet hence the post. Should i see if it gets better or do i take him to the vet asap. follow up question, is there other affordable options for at home treatments?