B737-800 Captain reported a track deviation occurred on departure from DFW during a wake turbulence avoidance maneuver.

Narrative

After takeoff encountered wake turbulence from the previous departure. To avoid further wake turbulence I climbed on runway heading. I tried; after climbing to what I thought was an altitude above the wake of previous plane; to get back on track but encountered wake turbulence again. At this time we finished the clean up and noticed we were off track to the right of the RNAV track. As we started to return to the track received a call from ATC to come left to a heading of 090. After further vectors we were informed to give ATC a call. After calling was informed we had a loss of separation with a departure from the west side. We did not receive any RA or TA advisories or indications. Loss of situational awareness with relation to the RNAV departure track as we were trying to avoid the wake turbulence. Lack of communication with ATC as to what we were experiencing. Greater separation on takeoff; however communication with ATC could have prevented this situation and maybe an early turn to be on the left side of the wake turbulence.