Questioning your self-worth is normal. I'm 42 years old. I've
   done it my whole life. Part of happiness *isn't not questioning*
   your self-worth. Allow yourself to question it. Bringing it out
   to others can also help as well, as you have done here. Around
   and around certain thoughts like to go in our heads; getting it
   out of your head is critical; poetry may help. Just start
   writing and keep doing so; whether you share it is up to you of
   course. Now, will someone go out with you? Let's flip it around:
   Would you go out with anybody? You've said that you're asexual;
   and there's nothing wrong with that. How you describe your
   sexuality is a word; an idea; straight, gay, bisexual, asexual,
   omnisexual, pansexual; is it sexual preference or gender
   identity? I've heard a wonderful phrase: gender fluidic. I love
   it because it takes the 'sex' out of the equation altogether.
   Dating; well, I'll ask again: would you go out with anybody? Do
   you have a vision of a partner? Perhaps, it is possible that you
   do not hold importance to the concept of "my one and only", yet
   have this nagging doubt that perhaps there's something amiss
   with _not_ feeling that strong "need for a single other".
   Perhaps it is community; you wish for closeness in *general*? Or
   perhaps you do wish for "that special one". Are you worthy?
   While you may have had bullies, you are the harshest critic and
   greatest forgiver of yourself that you will ever know. You bully
   yourself more than any bully ever could, and you forgive
   yourself more than the most loving of partners; each in
   different ways. Your view of yourself may or may not be
   accurate; Will you date anybody? Will anybody date you? Of
   course it's possible! But dating is goal-oriented stuff. Perhaps
   someone will come along and sweep you off your feet and turn
   your world upside down. But... are you ready for that were it to
   happen? And perhaps it won't. If someone sweeps you off your
   feet, are they the right one to do so? What if they are
   manipulative? A user? Secretly passive aggressive and before you
   know it, you're in a trap? These are the kinds of things
   everybody worries about in relationships to some degree, at
   least once in a while and entirely normal to consider. So are
   you lovable? Certainly. Perhaps find some adjectives to describe
   yourself with. Quirky - does that work? Eccentric? How about
   that? Find the words that describe you; we are all salesmen of
   ourselves and we choose the words we market ourselves with.