I'd second Fergie's advice on this. I gigged for years with a pain similar to what you're describing and now have some permanant damage in the left wrist because of it.
We don't have the same pedagogical tradition on the electric bass that we do on the upright because the instrument is still too new. Also, as pointed out in the video Fergie supplied, there are still too many technical variations among the EB's current virtuosos to really nail down what is a "correct" technique for everyone.
But I think we're starting to converge on what's a "natural" condition for the wrists and hands and that that is a good starting point to defining a "correct" technique for an individual player. We don't have it completely worked out yet, but we're finally starting to get there. Unfortunately, I'm a little bit of a casualty of the "wrong" technique, but the attempts to keep the little I have left have been fairly fruitful.
What I've adopted lately after trying a bunch of different things:
- left hand technique similar to that used by Carole Kaye. The video cited here by Fergie and Adam Nitti's link show a similar method. Basically, whatever it takes to keep my wrist straight and the thumb tending to point towards the headstock. I personally don't use the "pivot" method Carole Kaye talks about because it does crease my wrist too much. Otherwise, I use pretty much the same method.
- right hand technique is the floating thumb illustrated by Todd Johnson. I watched Todd's video on the FT and it was an absolute revelation. I was developing problems in my plucking hand too and this completely eliminated the problem (as well as gave me a good muting technique I can use on any bass).
- whatever instrument that allows me to maintain those positions. Specifically, this involves a will balanced bass (which is one of the reasons I use the Carvin Bunny Brunel).
In other words, I've found for me personally, the natural positions of the wrists and hands to be the least punishing when playing. That doesn't hold for everyone of course, but it works for me so far and has allowed me to resume playing on at least a limited basis.
Finally, don't be afraid to give up the 6 string if you have to. My main bass up until a few weeks ago was my Carvin Bunny 6. But just recently I've found myself drifting back onto my G&L L2000 because I just can't make the 6 work with my left hand over the long term. I can get close, but eventually I have to put it down.
So I finally broke down and ordered a 4 string version and have gone back to my L2000 in the meantime till the Bunny 4 gets here. Those will probably be my main basses from here on out.
My motto, instead of "correct technique", is now "whatever it takes". Basically, whatever it takes for you to mash the strings down on the fingerboard _without injuring yourself_. Anything else is B***s*** in my book. Find the non-painful method that works for you and develop that. Ditch those methods and instruments, etc., that don't work ASAP. Don't listen to anyone, no matter how famous or accomplished, that says "you must do this or else" - run, do not walk, away from those instructors. Go instead to guys like, well, Fergie,
, who say "lets find the right technique for you".
Well, you get the idea.
LS
Proper Technique for 6 string? 
So let me just give you a quick background then I'll tell you what my problem is..
And by recently I mean around 2 to 3 months tops, and I'd say I'm pretty good for being this new to bass. I play a lot of Chili Peppers and I'm trying to learn some Claypool 
So I decided to get a better bass than my no-name starter bass that I got for $40. I found an Ibanez SR506 6 string bass (around 03-04 model) on craigslist for 220 so I picked it up real quick and in a hurry! It's a great bass, needs some cosmetic work and new strings but it plays great! 
(I'm only 20 btw, and do my hand stretches often) but I'm not sure what the problem is... It almost feels like I put too much strain on it or almost like a bone that needs to be popped. It's not really a sharp pain, it's more of a soreness and it feels kinda swollen(it's not though just feels like it). So if ya'll can help me figure out what I'm doing wrong I'd really appreciate it! Maybe I just need to work my wrist muscles more so my hand can withstand the pressure. And the only trouble I have with the bass is playing the B string near the lower frets. I also didn't have this problem with my 4 string, but I didn't really use the "proper" technique either, I just did whatever was most comfortable, but on a 6er you don't really have a choice lol
