Plantar fasciitis and swaying. Worried?

I am suffering from Plantar fasciitis. I started icing regularly twice a day, wearing comfortable footwear, started stretching and using anti inflammatory gel and I can see the pain is subsiding. But since a few days I have started getting a swaying feeling as I walk and sit. It feels like I am in a boat. The feeling is not affecting my life as I can walk properly and I don't experience any head aches. I also tried balancing on a single leg and had no problems at all. I googled the problem and found out that due to an injury in one leg the body's balance is mostly on the other uninjured leg and the centre of gravity shifts a bit which results in swaying feeling. Can you explain if it is true ? If not what is the possible solution? Will the swaying feeling go away as my leg heals completely ? Should I be worried?