I had my tongue pierced back in high school. The actual piercing of your tongue will not hurt at all. You do not have nerves on the inner parts of your tongue, just on the outter. You won't feel a thing. What you will feel will be the clamps they use to hold your tongue in place. Depending on how long they take to pierce you, they shouldn't be on long, so it shouldn't hurt you too much. The pain from the clamps is bearable; it is not bad at all.
My tongue did not swell, surprisingly. I was talking just fine. People called me the following day to see if I actually went through with it and nobody believed me because I sounded normal. It is different for everyone though.
As for your web coming up near the front, they pierce your tongue at an angle. I'd go and talk to an artist to see what's up.
BEST OF LUCK!!
Oh, and like KDatUTC stated, no drinking for a while! I hated that about getting pierced! I was D.D. for a good while after that!