I doubt that the fear of rejection is really what's causing you to not approach. You risk rejection when you apply for a job or ask to borrow a pencil, yet you do this things with impunity. The problem is the guilt, shame, and self-blame placed on having to approach a woman. If you can change the way you think about what;s going on, it should help.
You are a guy. You know women usually don't approach guys extremely directly. You know women don't approach guys at all unless there is something interesting about him. If women NEVER sit by you or NEVER place themselves in your proxemity, then you will beyond any shadow of a doubt need to both approach women and continiously work on appearance/being interesting. There is nothing abnormal about this. The problem is (likely) that you are too normal. So if you are normal and need to approach lots of women, then why feel guilty? What is there to feel guilty about by being normal? It would be abnormal for you not to approach. Feel guilty for not approaching if you must, but certainly don't feel guilty for doing something completely normal (approaching women you *might* *possibly* be interested in IF (and only if) they turn out to be interesting and have excellent teeth, hair, skin, and interpersonal skills. Approaching doesn't signal you're interested, approaching signals an outside chance that you could possible have the remotest interest in her. If she does anything you feel removes that fleeting chance of interest, then she has failed your test. On to the next one! I don't follow up on dozens of approaches per week because I am happy with my LTR. Do you know how many women are out there right now wondering why I didn't follow up after it seemed to be going so well? Why do you think women are always frustrated and saying all the good ones are taken or worrying about their looks to get approached more??? The bar is set incredibly low, add to that guys like me who are taken get their hopes up only to be let down and find out we're taken all the time, and you have a bunch of frustrated women who are lucky to be approached at all by a guy who is even moderately cool, not a (borderline) street begger, and available.