You're right, I can't give medical advice. But having abnormally long or short circadian days is a known thing - called circadian diseases. It's not really my specialty, so I can't comment too much on it, but my understanding is that many of them are genetic. These genetic variations can cause the circadian clock to run slower or faster than normal (which happens to be adjacent to what I study, so I can talk about it in excruciating detail if desired)

The Familial Advanced Sleep Phase Syndrome (FASP) is one such genetic circadian disease that gets a lot of attention among the circadian field, but you almost certainly don't have it, since FASP makes your clock run shorter than 24 hours, whereas you seem to imply that yours runs longer.

The key thing to remember is that the circadian clock is not psychological. There is an actual, physical, molecular clock running in your brain and in nearly all the cells in your body. If this clock has imperfections, then that will directly lead to consequences in your circadian rhythms and your sleep cycle. The circadian clock is a real thing that people with the right equipment can measure and read. It wouldn't even be particularly hard - just a blood sample or a swab would be sufficient. To be honest, I myself would like to study your cells to see if there really is anything out of place, but that would probably break so many research and ethics rules.

Anyways, to answer your question, I would recommend getting a medical opinion - it might be worth specifically bringing up that you suspect you have a circadian disease. I'm not too sure about treatment options, since my impression has generally been that we kind of don't have any treatments for circadian diseases. But it's not really my specialty, so maybe there is. My memory is that melatonin is a masking cue, which basically means that it makes you sleep but it doesn't actually affect your circadian clock (which probably explains your poor experience with melatonin).