Hey welcome!
Great question. Definitely something it's probably kdai to speak over with someone who you can be really honest with about your struggle, and your mental state. I would highly recommend reaching out to one of the amazing mentors here, Hashem Help Me (HHM).
My take, as someone who goes to the mikva about twice a year, is that I really like the idea of going against your feeling of "not feeling like a person" before the dip and skipping the mikvah might be a very valid way of doing that (chassidisch poskim may have a different view

)
At the end of the day, no one alive (or almost no one) can "feel" kedusha/tumah/holiness. There's a good chance it's the feeling is some form of religious guilt/anxiety and "exposure training" can be helpful for that.
But that's just my gut feeling, and I do think it's worth talking to HHM about this.
Hatzlacha!