-- I get it. And if it helps, you are far from alone in this and certainly not the only man out there who finds this happening. A lot of women feel the same way about the men they meet.
First, find a 'peace' inside yourself that reassures you that no matter what happens, you are fine. Even though you might not think so, your feelings of urgency or insecurity (not wanting to end life alone) may be telegraphed in the most subtle of actions or words. It's that instinct we all have that picks up on these things. I'm sure you know when a woman you meet is on the fast track to get a husband.
--- I know the word might be overused, but getting even 4 sessions of counseling in to uncover the tools inside of you that can be used to provide your own comfort and security is well worthwhile.
Now, as for where to meet women? Go where the women go. Pick out the type of events that typically attract women and get yourself involved. With the right selections you could end up being the only rooster in the henhouse.
Local craft stores often have classes on everything from painting (pictures) to making quilts. By joining them you not only have a soothing outlet, a new and unusual hobby (although there are quite a few current basketball players I understand have taken up knitting and crocheting), but it's one of those situations where you'll stand out.
Check out www.VolunteerMatch.com for all sorts of volunteer needs in your zip code. You can choose something blatantly appealing to the ladies and kill two birds with one stone: Meeting new people and giving your efforts to a cause.
PLUS, volunteer efforts are a great way to learn things completely different from what you're used to. Office workers can learn how to work with horses; ditch diggers can learn how to fix computers. You get the idea.
Importantly, the point is to make meeting someone for that lifetime committment less significant to you than expanding yourself and your horizons. It's the old chestnut: When you stop looking for it, you'll find it.