My guess is that you meant to say that it has been caulked, not corked...

Short of taking out the tile work, here's what you should do:

Clean all of the existing caulk completely from the joints. Use a single edge razor in a holder to get it all off. Be careful that you don't gouge or cut the tub.

Use a mild cleaner to remove any soap residue, etc. from the area.

Then fill the tub with water so that the gap between the tub and the wall is as large as it's likely to be.

Caulk the gap with clear or white 100% silicone caulk.

I normally don't like 100% silicone caulk because it's hard to use and clean up, but in this case, you need the flexibility.

Let it cure 24 hours if you can before draining the water. Make sure that you get all of the joints including where the walls meet each other, down the sides of the tub and the base of the tub.

Also consider corner "splash guards" that keep the water from running along the ends of the tub and on to the floor.

Silicone is messy, so you may want to use masking tape to outline the area on both tub and wall. Then apply the silicone, then wet your finger and "tool" it (smooth it), wiping off the extra onto paper towels. Wet finger each time and keep going. Then immediately and carefully remove the masking tape. With the tape removed, you may want to wet your finger and smooth it lightly one last time (get's rid of edges when tape removed). Sounds like overkill, but does a nice job.

Is silicone caulk OK to get on your skin (i.e., finger)? I've used latex gloves and they seem to work. I'm paranoid about injury.

Also, why do you wet your finger before you tool it?