The Communications Act of 1934 bars carriers from charging unjust or unreasonable rates.  47 U.S.C. 201(b). 

It also provides that "[a]ny person claiming to be damaged by any common carrier . . . may either make complaint to the Commission . . . or may bring suit for the recovery of the damages for which such common carrier may be liable under the provisions of this chapter, in any district court of the United States of competent jurisdiction . . . ."  47 U.S.C. 207.

But may the person who pays a rate that section 201(b) prohibits jump straight to district court, bypassing the Federal Communications Commission and an FCC ruling on justness and reasonableness?

No.  N. County Comm. Corp. v. Calif. Catalog & Technology, No. 08-55408 (9th Cir. Feb. 10, 2010).