Socially anxious around my own friend

Hi all. Long time viewer, first time writer. I have major issues relating to social anxiety and low self-esteem, and this makes it very difficult for me to make or sustain relationships. It is often to the point that I look for evidence that others hate me as much as I hate myself, even if this 'evidence' is based in reality or not. I essentially believe I am a dead weight to everyone around me and have zero positive qualities to offer anyone.

As an example, I recently attended inpatient care for anorexia nervosa [unusal for a guy, but whatever], and I met a woman, let's call her Megan, who had very similar struggles to me with respct to body image and food. We got along well and learned that we shared many common experiences even outside of the eating disorder [we both speak French as a first language, we're both teachers, a few others]. We left inpatient care on the same day and exchanged phone numbers, agreeing to stay in touch as friends and supports to one another for life on the outside. We even offered to Skype with one another during difficult meals to ensure we actually ate.

Even though out relationship is entirely platonic, Megan suggested we remain friends, saying I am 'funny,' and 'a really cool guy,' [I do not believe either of those things], and she is the sweetest, most kindhearted person you could meet, yet she also has a great sense of humor and is just generally a very fun person to be around. Still, I have never been able to work up the nerve to suggest doing anything, as she also has a lot of friends and I can't help believe all of them are more intresting an charismatic than me, so why would she spend her time with a loser like me when she has other options?

Coincidentaly, my phone recently broke and all my contacts were lost. I forgot her phone number and I am far too much of a wimp to even try something like: 'Hey, my phne broke, any chance I could plug your number into my new one?' because I fear she will reject or otherwise humiliate me, or just generally not want any contact with me at all. As such, we no longer text each other and only see each other very rarely, such as when we happen to have a group together during outpatient care. Even then it is obvious that the friendship is weakening, as any relationship does when it is not maintained.

The easy solution, of couse, would be to simply grow a pair of balls and try something to the effect of: 'Say, Megan, any chance you'd wanna do [activity] later on this week?' but the other side of my brain is telling me: 'She doesn't like you and never has. She knows far more interesting people than you, you loser. Don't even bother asking, she'll only say no. Who'd want to be seen with a moron like you?' and so I ultimately do nothing. And of course these feelings are not exclusive to Megan, they apply to virtually everyone I become close with, so I generally remain aloof and distant.

Any thoughts on all of this?