I have heard of other guys who did/do not care for their red hair. Coloring seems a good immediate solution.

I also often feel like a third wheel, the odd-gal out -- and I, too, am introverted.

When I am at my best, I have used this tactic: I approach another person at a gathering who is alone and looking awkward. Sometimes the person is interesting, sometimes not. The person is always glad to have been recognized, and I feel better about myself because I helped out someone else in the same boat as I am.