I'm told that pits, especially young pits, tend to have sensitive skin. My pit Winnie has had several rashes, bumps, zit-looking things, etc. Most recently she had a rapidly growing wart like thing on her ear and the hair over it fell out, it was gross and scary. I took her to the vet and he said that it was no big deal and that it would go away. A few weeks later it did indeed go away and the hair grew back.
That said, I by and large agree with the post above, it's always best to get a professional opinion when possible. Expense is a concern for me as well, I want to provide the best care possible for my pet but it's sometimes hard to determine what "best care" is, I think I'm fortunate to have found a vet that I trust to advise me on this point.
My general rule of thumb is that if the dog seems to be feeling/acting Ok, it probably is OK. If Sypmtoms persist or if the condition rapidly deteriorates I try to get the vet on the phone for a consultation.
I hope everything turns out well for you and your pooch!