We have definitely had similar posts, do not be too worried.
Having a history of PSA results is really useful. They have not indicated a slow steady rise, so this probably is not cancer. To go from a PSA of 3 to 12 in six months would imply a doubling time of three months. It is true that, that is possible for prostate cancer but usually that is only in the later stages of the disease.
It is plausible that your PSA reached 50 in October and is now heading down. I am inclined to say that another PSA test four weeks after the 12.54 would provide a lot of information, a rise to about 16 would be entirely consistent with a PSA doubling time of 3 months, that would be worrying. A fall would be very good news, staying close to 12.54 would be reasonably good news as it would suggest there is no pattern of doubling.
I assume the urologist will do tests for infection and may prescribe antibiotics to try and rule out infection. There isn't much point in worrying, because worrying is not going to change anything.