Medicine dosage can and should be adjusted to fit the patient. Any doctor who doesn't do that is an idiot and should be avoided.
My non-medical advice is to try and find a doctor that works with you every step of the way as partners trying to solve an issue rather than some obnoxious high-horsed cunt that orders and expects complete obeisance.

I am in the same boat. I generally attribute it to a history of abuse by my parents and negligence.

even if I just slightly feel like one dislikes me a little

This line stuck out to me because of what I'm currently working through. I have no idea if we share this issue, so please take this with a grain of salt. Is it possible you struggle with people pleasing? If you perceive yourself to only have value when others are pleased with you, someone being displeased with you hits like a freight train. When someone gets mad at me on the road, even if it's not my fault, I can't stop thinking about it for MONTHS. It made me cry a lot as a boy. I don't think this accounts for all of what you're talking about, but it could be a piece of it.

One thing I learned is “scheduled worrying”. Or, “scheduled crying”, too. When something happened I had a strong emotional reaction to, tell myself I’ll let myself process it when I get home from (or whatever), and have time alone.

This probably won't fly here, but I was a "sensitive" child. I cried a lot about anything, threw fits, left birthday parties or sleepovers if I was mildly offended, pretended to be sick to avoid seeing people, etc. I got sick of it, joined sports, taekwondo. I cried a lot. I failed a lot. I eventually stopped, as my confidence grew. I taught myself through action and observation of my peers that I had no reason to be sad, I was just experiencing life.

I carried this later in life joining the fire service. Academy, and my probation year were super tough. Lots of hazing, and obviously physical and mental professional challenge. Once or twice the insults were sharp enough I felt tears welling up, but was able to reflect on my past confidence, channel my emotions into effort, work, etc. I used their insults as fuel, and became better.

It's not perfect, and not for everyone, but exposure worked for me, by eventually doing 2 things:

1. Show me that everyone experiences this. And that I'm no different. That I can do these things.
2. Repeated exposure trivialized things I took seriously as a kid. Simultaneously building my confidence.

I'll admit I had a good family, and a girlfriend during fire academy, so I always had someone caring about me at home, so I could "rest". That probably makes this approach more reasonable.

Could be ASD, could be CPTSD or PTSD. Have you talked to mental health practitioners?