Richardson is a great school district and that seems to be where you are right now. There are lots of apartments in your price range. You may also try Plano. Try this, just an idea, go on Craig's list and see what you can find. There are apartment locator services that will help you for no fee to you. If that doesn't help, give me a call at 214-534-2020 and I'lls ee what I can find in MLS. But I really think your best bet is a locator.
Best of luck to you and your daughter. Hang in there!