If it's a Canmore (Gore-Tex(R) ) bag, you might be able to use cyano-acrilate (SuperGlue) to seal the gaps in the seams. Just run a trickle along the seam and let it dry. I had a leak in the back corner of my Canmore bag, used some CA and haven't had a problem since.

If it's a leather bag, it sounds like you may need to re-season. If it's a 'hybrid' bag (artificial inside and leather outside), check with the manufacturer on what to do if you detect a leak.

For the leak around the 'neck of your chanter', do you mean it's leaking at/around the chanter stock? That may just need a little more tightening on your tie-in. You can get some artificial sinew (check Tandy leather), and tie a couple more wraps on it.

Use the following method:
1) Wrap some sinew around a 1" dowel rod (or broomstick) and place the rod on the floor
2) Tie the sinew onto the chanter stock (and around the bag as well) with a clove hitch (look it up - it's not that hard to tie)
3) Make one wrap around the chanter stock
4) Place your feet on the dowel rod and pull the sinew as tight as you can
5) Repeat steps 3 and 4 a couple of times
6) Tie off the sinew with a clove hitch

You might also use some extra tape there to help finish sealing the chanter stock. I used plain old electrician's tape (same stuff I use on the chanter to flatten notes buy covering the hole - I just cut it in half width-wise for the chanter).

That was done with mine early on (I didn't have the knowledge at the time, so a senior piper in the band did it for me). Haven't had a leak there since, either.

Good luck!