Don't panic! It takes a lot of practice to do volume swells (AKA "violining") properly. It's damn easy when you've put in the hours though; like riding a bike. I learned how to because I had heard a solo by Rush's guitarist, Alex Lifeson, on the live version of XAnadu on Exit Stage Left and thought it was the most gorgeous sound ever. I didn't even know it was guitar to start with!
First point: put the volume up quite far on your amp; this means you won't have to turn the volume knob so far with your finger.
Second point: make sure you're holding your pick correctly. When I first started learning I had to change the way I held my pick - I had held it between the tips of my thumb and first and second finger. (This also made pinch harmonics harder.) Then I changed and started holding my pick properly between my thumb and the curled, tip-most knuckle of my first finger.
Third point: start with the volume down and rest the inside of the second knuckle of your little finger on the bottom of the knob. Pick the string(s): to start with pick single higher strings because that's easiest.
Four: roll your little finger back until just beyond the tip most joint so the volume swells. I find that this naturally moves the pick away from the strings. It may help to rest the outer edge of your hand behind or on the bridge (unless it's a floating trem which makes life harder)
Five: rapidly slide your little finger back to its starting position.

That's it really. When you're really good at this try it with pinch harmonics.