Yes, the battery should go post haste. Also, you'll maybe want to look into ways to fully discharge it safely before doing so (not with salt water, btw). Since it's swollen, that means internal damage and a potential for it to burst and start a fire. Don't want that happening in the garbage truck or at a battery drop off location!
As for the touch issue? Who knows right now, but it should be the least of your current problems. If replacing the battery doesn't fix the problem, then there are other possible issues at play. The screen digitizer picks up touches via electrical impulses in your skin. Anything that disturbs those impulses will cause touch response issues. That can be unstable battery voltages, bad chargers and cables, or damaged hardware within the phone itself. The battery swelling can cause the last issue there, so replacing it has the potential of ruling out 2 issues with your touch response.