I'm not a professional, nor am I saying it's completely psychological, but some people have what is known as Body Dysmorphic Disorder. It basically warps the mind into thinking a part of the body, or the whole body itself is deformed or hideous and unnatural. It's not that the people who suffer from this disease are in actuality deformed or monstrous in appearance, but they are so convinced that they are beyond what they perceive as "normal" in appearance that they hide from the world, even avoiding such things as looking in mirrors or getting their picture taken.
You say you appear as though you've been born with a cleft lip, but had no corrective surgery? I don't mean to make you focus further on yourself and drive your anxiety and insecurities higher, so my apologies. I wouldn't focus so much on surgically fixing it if you can eat and talk just fine. Besides, some people focus so much on trying to make themselves perfect in appearance that they become obsessed with having one cosmetic procedure done after another and wind up looking a lot worse off then where they started. Not to mention they look all fake and plastic-like.
I haven't seen a picture of you, nor am I asking you to give me one. I know you're probably not comfortable doing that now. However, I am going to say that we are often way more critical of ourselves than others are of us. I know you said you can't afford therapy right now, so I really feel for you. A good therapist can help boost one's own self confidence and help work through whatever insecurities we have.
I wish I could help you feel better somehow.