Veering to the left on the swim

I am a self taught sub par swimmer.  Just for fun, this morning during my swim session I tried swimming with my eyes closed to determine how my line was.  I knew it was not going to be straight but I was shoked at just how not straight it was.  I have a severe problem veering to the left.  Obviously there is a muscle/technique imbalance at play, not surprising as I only breathe to one side, but what type of imbalance casues me to veer to the left?  Perhaps a stupid question but is it that my catch and pull is stronger on my left side than my right and that causes me to veer to the left?  I breathe to the right side and always considered my right hand catch and pull superior to the left, so I am having a hard time grasping how my left side has a stronger pull.  Finally, what is the best way to fix this problem?  Technically I have few issues breathing bi-laterally, but I can't  get enough air to breathe every third stroke for any significant distance and switch to breathing every second stroke.

Thanks in advance for your help.