Hi,
I LOVE your question.
I go to school for psychology. My last psych class was Abnormal Psych (all the disorders).
I have always been a self-diagnoser and one to diagnose others (tip: be careful who you diagnose...some people dont like it, haha.)
I diagnosed myself with panic disorder maybe half a year ago.
A few weeks ago, I diagnosed myself with bpd.
I own the DSM 5 and even w.o it, it is easy to find the dsm criterion for each disorder so one can see exactly what is needed to have a diagnosis.

The only problems with self diagnosing are 1: personal biases (people often see themselves differently than how others see them-to put it briefly) and 2: the person may not have an accurate understanding of the criterion needed for diagnosis.

If those two things are not an issue, there is no problem or necessary fallacy with self-diagnosis.