My dad's sole (pad) of right foot has become bulgy since 3 years now and so he cannot walk in balance. it looks swollen, doesn't hurt but increasing.

Get it checked: There are several reasons for a bulging foot. It could be severe swelling or even a mass of some sort. Even without pain, this should be evaluated promptly by a podiatrist.

Sole: Would suggest an MRI but could be a fibromyalgia which usually are in arch area but can be in other locations. Their are many possibities so MRI would help.