Yes you can bring frozen ice packs on board the plane in your hand luggage.
The store bought ice packs that are sealed are not considered hazardous so you can bring them on the air plane in your hand luggage or in your checked luggage.
You may be limited to the amount of ice packs you can carry on in your hand luggage but you can bring as many as you reasonably need to in your checked baggage.
If you bring the ice packs on the plane in your carry on luggage you need to make sure the ice packs are frozen solid before you go through the security check point.
If the ice packs are thawed out when going through security they won't be allowed but as long as the ice packs are frozen they will be allowed through security.