The great struggle
"The logical part of me says that metaphysical things are not real, however, the other feeling part of me says that they are real."
I struggled with this for a mighty long time, and can still go back into 'Gosh, how embarrassing, I made all of that up!" The last several years I am more stable in accepting this is going on, and hence take better care of myself and get onto things quicker to flush them out, disassociate from them, etc. But for me it has been a long journey just to get here.
I've hinted around this to a therapist I used to see, who was aware I had a very reactive nervous system and considerable past trauma and put it down to that without blinking too much of an eye - but expect most medical professionals would think I was delusional if I went into explaining it full-bore. So I can relate to your hesitancy. It is a dilemma.
"How do I reconcile the two parts of myself? Maybe I am crazy "
I think that is a healthy question to keep in mind. Too many people do some quiz on the internet and next thing it's "OMG I is empathy!" I think I finally wore my doubts down by collating so much evidence. I keep a journal recording various things anyway and am very much aware of my baseline state, and then the major changes that are care of miscellaneous pick-ups stand out (I still check I'm not conflating/imagining/projecting my own stuff). Sometimes I think, what if I die, whoever reads this will think I'm mad!
Maybe start acting as if this IS real - you can always change your mind at a later date...
I think daily grounding, centring and recharging of oneself is very important (for me, at any rate). Maybe introduce a care package for yourself that you do every day - whether that is a brief period meditating, showers or baths taken with intent to cleanse and rebalance, light visualisations, prayer, intention setting and affirmations, flushing as well as grounding and shielding, etc etc. Baths also help me with chronic pain - I add Epsoms, sea salt, and bicarb.
I find Caroline van Kimmenade's videos and articles helpful and calming. If you don't know her site, here is a link:
Where she goes into Empaths and Worldview further down the piece, I think is really important. She doesn't give any answers, really - unless you shell out for her expensive coaching! I am not sure there are any real answers for this, but we figure out our own way with it, eventually, amassing information and little tips and tricks; some work, some don't; slowly, slowly, I think.
Good luck with your employment. Getting calm and centred in your (painful) body, day by day, and looking after it and you is the best advice I can think of from my own experience. Courage!