Hello AliQ ...and welcome to PC!
Yeah the other poster already said it your issues with looks could be related to Body Dysmorphic Disorder too. I do have issues in that direction too, I think us AvPD folks are just more vulnerable for that kind of conditions...
It's good you're questioning your diagnosis. I know a lot of people who have had totally different diagnosis from different professionals until they finally got the right one...
Yes, AvPD is pretty much totally about self esteem issues.
Coping with inadequacy... For me it helps that if someone compliments on me, I will tell myself to keep this compliment in mind and remember it more often... don't know how to describe that really... normally, I will "forget" positive things said about me very quickly, because I think "ain't be true anyway..". Trying to value good feedback is some kind of mindfulness I guess. Another thing is, if you can handle to have one or two friends, which I know is a major challenge for AvPDers, it helps because when you know someone more closely you make this experience that people aren't as flawless and perfect as they look from afar... and that the flaws you see in yourself aren't as unusual or "unforgivable" as you might think. At least for me it was always like that, if I had relatively much social integration (life time record = 3 friends at a time) my self esteem issues weren't as bad.
Hmm.. otherwise... this may be a bit melancholic... but I've made my peace in a way with being inadequate by giving up on always compulsively comparing myself to others and too, there's like two or three things I think I am "better" in or at least subjectively speaking good at in comparison to others, and I can sort of reconciliate with being an "omega" because I can tell myself that I have some good qualities on myself too.
The last thing that comes to mind regarding dealing with AvPD is "equanimity". By that I mean you accept your suffering without trying to devaluate or deny it exists. It's like theres two ways of dealing with suffering, the first is like a sulking child sitting in a corner which says "if I can't have what I want, I don't want to engage at all". The other kind means to go on though it hurts... accepting pain, being compassionate towards self while at the same not being bitter about having to suffer.
Hope that was somehow helpful, at least in parts...