B737 First Officer reported flap malfunction on short final.

Narrative

On ILS to runway XXC; we had received our landing clearance to land runway XXC hold short of taxiway 1. Pf called for flaps 30 landing checklist. It was then that I noticed that the flaps had been selected to flaps 30 position and was indicating flaps 1 with a in my opinion a perceptible split. I verbalized the flap malfunction; pilot flying called for go around. During the go around we were issued instructions fly the localizer outbound; climb maintain 2500. As we were working through go around process we were issued a heading clearance and to climb and maintain 4000. I put 4000 in and pointed to the altitude where it was confirmed. During the go around in the stress of the situation the aircraft exceeded 4400; before being corrected to maintain 4000. The Captain requested priority handling; I became the PF as the Captain began PM and initiated the QRC flaps trailing edge flaps disagree checklist. Once the checklist was completed it was decided to return to ZZZ for the ils XYC. The landing was uneventful; we communicated that with emergency vehicles after landing as well. The aircraft and passengers were safely parked at the gate; with normal unloading process; and elb (Electronic Log Book) reports were sent to maintenance control.