Should a turtle be swollen and sticking out of its shell.?

Short answer: no. If your turtle's skin is swollen and bulging out of the shell, it is probably due to the fact that the turtle is not spending enough time out of water. A turtle does not live solely in water. Forcing it to constantly live in an aquatic environment causes the body to fill with moisture, causing it to swell. Give it sunlight and time to roam outside every day.