need help about maybe my cat getting mange!!?

okay i just rescued a dog from a animal shelter friday. i gave her a bath the next mourning since it was late when we got home and then today i noticed she had red bumps and scabs all over her belly so i took her to a vet. he gave her a shot for itching and some pills for 2 weeks for allergys and i said so this isnt mange that maybe my cat can get??? and then he didnt say anything for a while then finally said he could take a skin craping but its hard to find mange in a skin scraping so then he left the room and came back and said she did look like she had mange (after he gave me the pills and powder for skin and deworming) and said that if it doesnt clear up in a few days to come back so i said lets just treat her for mange now which he said was $35 dipping and he refused!!! he just wants another examination fee. anyways my cat has FIV i love him with everything i have and i am freaking out that if he gets it he might die because when you have something like FIV or HIV the smallest thing can take your life right!?!?! what should i do give my cat a bath incase of? my washing machine just broke today so all of the stuff the dog has touched is sitting there and i caught my cat laying on it im balling here please dont be negative just to be, but someone please tell me the truth on what i should do so my cat doesnt get it. i now i know i shouldnt have gotten a dog but i thought i was saving her life and i cant just go shove her back in the hole she came from but i am keeping her isolated from my cat. i read on a site cats cant get it from a dog unless its touching it frequntly but my cat is a big baby and last night curled up on the couch with me and the new dog and im so scared. i’ve done so good keeping my cat healthy for so long with this fiv and now this. im so scared. he litterly is my child. what should i do for him to stop it now!?!? btw right before i left the vets boxer(dog) came out and was sniffing my dog and the vet grabbed him by the collar and locked him in a room away from my dog, like hello he even thinks she has mange but wont treat her for it?!?! wtf!!!!! does he not understand i dont want my cats to get it i told him like 5 times and felt like an idiot. he was so unfriendly too and just picked my dog up under her arm and carried her with one of his arms while she wiggled.

i don;t have an answer but i just want to say sorry 🙁 i feel sad for you, i have a cat and i love her to death so i can how you would feel.

Learn  more about Cat Mange here.