TSA makes it quite clear that you can be processed without any individually acceptable ID. It happens. Lost/stolen wallet and the like.

TSA simply needs to be able to otherwise verify your identity. A combination of school ID's, utility bills and the like, will allow TSA to run you through various government and commercial databases and you should be on your way.

Sometimes, such passengers do receive extra screening and the ID process can take a good while if things are busy. So, just allow time.