it seems set screw for single handle kitchen sink is corroded, is that why the handle rocks , if so would any local hardware store the item or do i go to a specialty plumbing center? thanks pv

the screw will either be standard or metric threads. both are available at a well stocked hardware store.
the same goes for the allen wrench needed. metric or standard??
the problem will be getting it out.
once out simply bring it and the handle to the store to get the right size.
P/S, a touch of grease will give you a fighting chance at turning the new one if it needs to be tightened in the future.

Do not use a ball-driver type allen wrench. The ball will snap off.

Would the next step be drilling out the set screw if you can't remove it? or is there another option?

Usually it is a hardened metal so hacksawing the handle off may be easier.

It's not fun, if the set screw won't come out. Depending on the handle, as hj said, a hack-saw can work. I've used a Dremel with a cutting wheel. I'm not a pro, I've just had the bad luck to have had this problem a couple times. Ask me how I know about the ball-driver.

The issue with getting the set screw from a hardware store is that they only have them in high carbon steel and steel screws will corrode and be difficult or impossible to remove in the future. Grease will only help for so long before it becomes saturated with water and then the grease will promote corrosion.

The original set screw is either stainless steel or plated brass and is best replaced with something similar.