Why do you feel you need a girlfriend to validate who you are?
EDIT:
hmm, that sounded meaner than I intended. What I mean is, you don't need a girlfriend to survive; its not like you'll literally fall over and pass into oblivion if you don't have a girl around your arm.
Sure, it sucks to be the third man in a group, hell I went to prom alone with five other couples. It was entirely my fault, I could've asked someone to go with me, I don't know if they would've said yes or no and I'll never know. All that matters is having fun. Don't let this stuff get to you.

EDIT 2
God damn. Enough psuedo-wisdom outta me.
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Great point. Relationships are not vital to everyone. And if you need a friend, (And judging from what I know from your friends already, I'm gonna assume you do), just get a normal friend. They do the same stuff, except women add in the sex part. And loving a woman just for sex is good, however, don't mislead her into thinking that you actually love her love her, when you really don't. Then she ends up loving you, and when you're tired of her or w/e and want to break up, It'll be extremely awkward and it makes you seem like an asshole when you do. Trust me, I've done it twice. It sucks.
As for the physical and mental pain thing, I picture them as really the same thing. They're both really mental. They effect mainly the mind. Except the so called phsyical pain, can effect another part of the body directly a lot greater. (Like a serious burn or severed limb) The question would be, which one causes greater pain over all, and that's all opinion. However, physical does cause more physical DAMAGE than mental. Mental may break your spirits, make you not want to live, and commit suicide. Phsyical could kill you right away. So looking at a stoic's point of view, physical would be worse. But I hate stoics. They're snobby wannabe emotionaless cliche robots.