Since, you're asking for personal reports, I may as well chime in.
I've managed to improve my ability to feel at ease when confronted with new people and places. This is something I did on my own, but like others have said, seeking professional expertise may help you achieve your goals more effectively, or may uncover things that need to be addressed in other ways.
It may help to identify which specific parts of social interactions make you uneasy. For me it was feeling like I wouldn't have anything to say in response and that an awkward pause would ensue. I often second-guessed myself and felt like my responses didn't have worth. If your situation is different, the rest may not apply.
The first changes I made were to view my situation as temporary. Instead of framing myself as a permanently awkward conversationalist, I framed my starting point as a challenge to build new skills. While some people learn these intuitively, I had to consciously build them[1]. By framing my challenge as a skill-building journey, I was able to make progress by seeking out specific information in order to build this skill.
There were three techniques I practiced to help me build this skill. Topic vectoring[2], open-ended questions, and question-statement balancing.
Topic vectoring is a simple heuristic for picking an appropriate response. A conversation response can go "up" a level by speaking more generally about the topic, go "down" a level by drilling down to a specific detail about the topic, or move laterally by shifting to an adjacent topic. Conversations progress by incrementally accreting small topic shifts. When too large of a topic shift is introduced, it is hard for the other participant(s) to follow along. This includes shifts that compose multiple directions. When I'm reaching for a response, I use this tool to pick an appropriate one.
You've most certainly heard of open-ended questions before. Practicing open-ended questions was a skill I made a point of developing by monitoring my proportion of responses and adjusting as necessary. Good questions are conversational expanders. They require little from the querent and little from the respondent. They can feel like a good layup when done right.
The same goes for question-statement balancing. Too many statements, and it begins to look like I just want to talk about my interests, and too many questions looks more like an interrogation than a conversation.
All of these skills fit together in a way that make me feel like I know how navigate conversations much better than I did before. Quickly, it's important to describe what they are not. They are not memorizing a bunch of conversation prompts. They are heuristics that can be practiced, employed tactically, and form a cohesive toolkit. I strive for balanced conversations where other people feel heard and engaged, and I can walk away feeling the same way.
Best of luck to you on your journey whichever path it takes. :)
1. There is probably some amount of neuro-atypicalness at play here, but that's not something I've explored too much.
2. The resource explaining this may be lost to the sands of time and it certainly went by another name.