It sounds almost certain that you were out of balance.
The 737 slip indications are punk so the only good way of doing it is to 'kick' (rudder) the control wheel till it sits horizontally.
Correct balance is the absolute key to flying OEI half-way accurately.
You have a tremendous amount in our favour that you have recognised a problem and are taking steps to recover. keep that attitude and you will get there.
I have to say though, I would have been a little disappointed with the attitude of your instructor/examiner if I had left a part failed OPC/LPC without receiving a full and clear explanation of the reasons and causes of the fail.
Did you get another go at that part of the test?