I know that we don't know each other very well. I believe we had a few back and forths in the debate forums and such. So keep in mind that you may have different views about what I feel in regards to this. But all of that aside, I really don't like how much pressure your mom is putting onto you.
Interestingly enough, I was in a very similar predicament back in high school. I never dated anyone, prom was coming, and my mom was in full force trying to get me to go. It baffled her that I could have no desire to make wonderful high school memories with a girl, blah blah etc.
But the fact of the matter is, I really hate the concept of prom. I don't know exactly how you feel about it, but I find it idiotic for a number of reasons. The main one being that It's a social expectation that tries to punish you if you show no interest. Not only was my mother a wonderful example of this, but a few of my friends were being pests about it as well. You shouldn't feel forced to go to a party that costs you money/energy/time when you don't want to. It's a lame ritualistic party. Therefore it is optional. Period.
Also, forcing yourself to find a date is nothing but a bad idea. If you already have a girlfriend that you really like and all, this is totally fine for prom. But you don't, and you're struggling to find a date. Honestly, even if you manage to force yourself to someone in time, don't count on things working out that well. Forced relationships like that rarely work out. Also, why is it such a big failure if you don't? You can't just put "find a date in the next two weeks" on a checklist. That's not how romance works. You don't have any control over things like that. It honestly is just plain luck if you find someone right for you. So don't stress too much about that, okay? You have to let romance come to you. Not the other way around.
So in short, there are three scenarios for what can happen here.
The first is you getting really lucky and finding a great girl to go with in time. This scenario would be great, but the odds of this happening are low. So you can't exactly count on this one as your main strategy.
The second scenario is you just going with some friends, and telling your mom to get over the date part and that finding romance doesn't simply happen overnight (at least, when you want it to.) This could work out just fine, really. Plenty of my friends did this, and they still had a great time. Dates aren't everything.
The third scenario is you telling your mom to completely get over herself and not go to prom. Do this if you simply don't like prom, and really don't want to go. This is what I went with, and I still don't regret it to this day. There is a line to be crossed in regards to interfering with your son's life, and your mother has crossed it big time. Put her in her place. However, your mother may not be happy with doing so. At all. If you think that doing this will piss her off a bit too much, then it might be best to avoid it. That is your discretion to know.
Also, the "bring prom to her" idea that Smocks has is kind of a great one? And super romantic. If you think that it's a good idea too, you should definitely go for it I think.
That's what I think about the situation as a whole. Regardless of what you decide to do, I hope that things work out!