Non-citizen traveling within the US after dropping off passport for visa [duplicate]

According to the list of valid IDs accepted by TSA, the government agency that handles airport security in the U.S., the only form of ID accepted for foreign nationals not holding one of many U.S., Canadian, or Native American ID cards is a foreign passport. Neither of the two forms of ID you listed in your question are in the list.

However, if you scroll to the bottom of that page, you'll see that there is a procedure for people who don't have valid ID on them. It's a fairly arduous process, involving collecting and verifying your personal information (which they will likely have due to your U.S. immigration process), and possibly some additional screening; you may not be allowed to fly if they aren't able to confirm your information. If you wish to fly, do arrive at the airport far in advance of your flight so you have time to complete this process.

There is (probably, I haven't checked) no ID check on Amtrak trains, so I recommend booking a train ticket. Besides, the train will probably take less time than having to arrive at the airport very early and going through all of that extra screening, with the chance of being denied access.