How can I stop believing my best friend will leave me, get bored of me, find me annoying, despite being reassured several times that won't happen?

Write down an affirming statement somewhere you will see it often -- on a notebook, on a sticky note on your bathroom mirror, anywhere. "I am a valuable, kind, adjective-of-your-choice person and worthy of love". You're afraid your friend will leave you or tire of you because you believe yourself to be ultimately boring/annoying/unloveable. It is much easier to accept that our friends care for us when we can recognize our own value and worth. And sometimes just repeating it over and over again until you believe it will do the trick. It's okay not to believe it all the time. Even believing it for a few minutes a day is a good start.

Change your way of thinking. Instead of all negative, fortune, fatalistic fortune telling, include maybe it will be all good, maybe it will all turn out okay, I cannot exclude the positive, nor the negative, that is the fact. When we see only the bad side of life, you'll ony see more terrible things. Surround yourself with motivational videos, books, people, don't watch who killed who and horror movies. At all. It all adds to the negative mindset. When you believe that you will experience bad things, you are right. When you say that you are going to experience good things, it is also the truth.