Sounds familiar, OP.
I'm 19 and I'm a pretty independent person who, up until a month ago, had never been in a relationship. Not really sure why, but I guess it never really appealed or anything. It's not something I really bothered about much - sometimes I felt a bit lonely when seeing mates in relationships but on the hole I was content and independent.
My self-esteem issues didn't really help me much either - I got into the mindframe that I wasn't attractive and was 'safer' alone (I don't really trust many people). Didn't really know how to respond when a guy - friend of a friend who I'd only met earlier that evening - started putting the moves on me in the middle of a club. Was a bit bowled over, but agreed to meet him for a drink the next day. Not because I liked him back *that* much at the time, but because I figured I didn't want to pass up any more opportunities. Wanted to see how it went, had nothing to lose. A month on, and we're together - still early days, owing to the fact that I left uni for hols a day after I met him and am flitting between 2 cities in my spare time - but I'm glad I gave it the chance. It doesn't have to damage your independence if you don't want it to. Am still determined no guy will 'clip my wings'. I've a job that isn't exactly the safest in the world - requires a bit of resilience and courage - and I think he knows I wouldn't give it up.
So yeah, go on a few dates, see what happens. Let it build your self esteem to know that guys who ask you out are interested and do find something attractive in you, even if you don't see it yourself.