Will ptosis surgery fix my eyebrow and improve symmetry?

True.  If you left eyelid ptosis is corrected, you should see improvement in eyebrow symmetry after a few months after it's all healed.  Initially, you might still use your eyebrow a lot to assist in eye opening because of swelling and/or habit, so the asymmetry might persist for a few months.  Good luck!

I cannot comment accurately without seeing a photo but it is true that a droopy eyelid can cause the same side eyebrow to raise in order to assist to lift it, which means the eyebrow should relax down after droopy eyelid (ptosis) surgery.

You did not provide a photograph so we are speculating here.  Generally, when there is a compensatory brow elevation in association with eyelid ptosis, correcting the eyelid position can result in a relaxation of the eyebrow position.  It is not guaranteed.  There are individuals who have retrained their muscles and correcting the ptosis has very little impact on the position of the eyebrow.  In these circumstances, botox injection can be used to help retrain the forehead muscle.

The short answer is maybe...Brow compensation for a drooping eyelid takes years to develop as the eyelid usually droops over a slow period of time. In those cases fixing the eyelid may or may not cause the brow elevation to improve. Usually it does but NOT ALWAYS. As an oculoplastic surgeon, I do just eyelids and so I treat a lot of patients with drooping eyelids and patients who have had a drooping eyelid surgically treated. In patients with acute ptosis (suddenly) with brow elevation that resolves 99% of the time once the drooping is treated but less so in chronic or long term ptosis cases. 

As you have noted you have a raised brow on the side of your ptosis to help compensate for the droopy eyelid. There is a good chance that this will correct itself after the ptosis is fixed however it may take a few months to settle back particularly if the ptosis is longstanding. If it doesn't then the brow could be temporarily lowered with some Botox or perhaps the opposite brow raised if that would give a better looking outcome. As there are no photos it is difficult to comment definitively but you should give things plenty of time to settle (several months) before considering adjustments to the brow