Is it normal to be afraid to make new connections

I'm probably afraid of rejection too, but I mostly fear dealing with annoyances, and being constantly disappointed.

I definitely understand your fear of rejection and it's a very normal and valid fear, however, it's not worth getting in the way of living your life the way you want to. It's an unfortunate fact that we all have to deal with rejection of some sort at some point in our lives, but it doesn't necessarily mean there's something wrong with you. Sometimes people don't click, people have personal issues within themselves, etc. It's just a part of life. If you don't mesh with someone or they don't mesh with you, that doesn't mean the next person will be the same.