Does anyone know where I can find a cute prom dress with sleeves that go almost down to the elbow?

I also applaud you for taking a modest route; prom dresses these days are often made to exemplify the woman's more female features, with little consideration for modesty. It's sad, really. Anyways, I would take a look at some cheap modest wedding gowns in the area, see what you can find there. Sorry I'm not that much of a help, but if I see anything else I'll put it here.

Good for you for going a bit in the modesty direction! I am actually shocked at some of the "barely there" prom dresses being sold! You can find these dresess at a few places!  One is Great Lengths where there is a really pretty prom gown selling for $125.00!
specifics:
This dress has beading on the bodice and gives this ball gown its feminine appeal. Delicate beads arranged in a floral pattern decorate the bodice, creating a perfect backdrop for the beaded accent at the waist. A matching shrug provides elegant & modest coverage.
Imported.

They also have the lisbeth gown that sells for $125.00
specifics:
An epitome of simple chic!! Half sleeve satin excellence with similar thread embroidery artistically done over the bodice. Empire waistline followed by an A line gown. This prom gown can be your cherished one!

Beautifully Modest has a cute knee length dress that sells for $165.00
specifics:
This knee length sheath cut gown is made from elegant charmeuse fabric with a bot-neckline, dangling sleeves and a gathered waist