If I had a kidney or UTI infection and no antibiotics, and symptoms are gone, does that mean it went away?

Possibly. Some utis including kidney infections clear up in time due to your own intrinsic body defense mechanisms. However, you should get your urine checked to make sure infection has cleared up ant merely become non-symptomatic. By & large all utis are best treated with antibiotics, both for speed of resolution and reduce rusk of infection spreading.
Perhaps. It could be. If all of your symptoms are gone (pain, fever, difficulty urinating, etc), then your immune system may have fought off the infection. However, you should be vigilant and if any symptoms recur or new symptoms develop, see your doctor to make sure it's not a recurrence or spread of the infection.