Help! i think my kitty has a broken tail?

my cat Bucko is a year old and has been very lethargic and not eating very much, hes normally a pretty active cat and he LOVES to eat, i noticed while petting him yesterday that it hurts him when i pet towards the base of his tail, when i felt it it felt like one joint of the tail is very swollen and he gets mad when i touch it. it seems like it is probably broken on that spot, but would that be a reason for him to be lethargic and lose his appetite? also i noticed a few days ago( right around the time he started acting weird) after i let him inside the house after letting him hangout in the backyard for a few hours that his collar was missing...i wonder what happened to him. i know the best thing to do is to take him to a vet but i am a new mother of a 3 month old baby on a very tight budget and really cant afford it, ANY advice on how i can help poor Bucko would be greatly appreciated