Some suggestions - could you borrow a dress? Buy one at a consignment shop? Or similar -- there is no reason you need a dress over $1K. We do not have financial problems (currently) in my family, but if my daughter wanted a dress for a prom that was over $1K I'd say go out and buy it yourself. That is more than what I spent on my wedding dress.
Another question, why is it so much more for a girl than a boy? I would think besides the dress, if a boy asked you to the prom, then he should be paying for the items such as transportation and prom tickets. If you asked then you should pay. However, if you decide to split the cost, then you could simply forgo some of the items -- no need for a limo. I love my daughter's school -- they do not allow limos -- things were getting costly, the school changed it policy. For students going to the prom, they need to take a bus from the high school to the prom and then return on the bus -- no overnight stays; late night crap. The idea of the night is the prom itself.
Do you have a job? Could you babysit or do some other type of work to get the money to pay for yourself.
But seeing now you cannot go -- why not come clean to your mom -- unless you do not want her to be hurt? Or just simply let her know you are really not that interested as it seems crazy to spend over a thousand dollars for one night when you could go out with a group of friends and just hang and have even more fun.
I honestly think the expenses of some of these proms get so out of hand, I am glad my daughter's school has ensured there are cut backs -- doesn't stop the $1k dresses, but at least all the extras.