This is for your ski locker drain. Don't bother with buying just a plug, if yours is like mine, they may not have sealed around the fitting itself, and may have screwed up the fitting, requiring the rest of it to be replaced. Double-check the fitment, but it is highly probable that even if it isn't listed for your boat, it will work for your purposes. It won't hurt you to have the surrounding fitting either, and you're only going to save a buck or three by only buying a replacement plug (if such a thing can even be found - I looked, and gave up).
If you are saying that you have to have the bilge running just to stay on top of the water, then no, that's not normal. If you are saying that you have to run the bilge pump so that you feel comfortable that you aren't going to sink, then you'll have to describe the amount of water that comes out when you DO run the bilge. It's one of two things, either YOU are abnormal, or the amount of water is abnormal ? More details on your situation.
If your bilge pump is pumping water non-stop, then you have more leaks, and seemingly pretty severe leaks at that, and they should be addressed before you take your boat out again.
Coming UP through the ski locker means you have a ton of water in the bilge. Make sure it's as empty as can be, by pulling it out onto the trailer, and jacking the front of the boat up as high as possible. Chock the wheels, and add some 2x4's or bricks or something to get the bow up higher than you normally would. You likely don't have all the water out from previous trips. Start with as little water as possible, then drop it back in the water, and see if there's now some water in the bilge before you even take off from the dock. Look through the inspection hatch on your cleanout tray. If you DO have water in there, your rub rail likely needs to be sealed, because you took on water before you ever left the dock - that's from dropping the boat in the water and burying the leaking rub rail. Alternatives that aren't as likely on a boat as new as yours is a broken or loose scupper, or....worse. Start with the simple, and work your way back to the more difficult. Empty lets you track what's going on, and helps to narrow down where you should be focusing on.