In your letter, you can then state your situation and ask help from the senator, for example, you can ask if your name check is clear. The senator's office has their own way to contact the FBI and the immigaration office.
At the same time, you can also send letter to the first lady who has a website and you can find her contact information too. Then send letter to her ask her help to find out if your name check is clear or not from the FBI.
So, you should try both ways, it only take two stamps. You have nothing to lose.
I hope this helps.