Oy. I can see why you’d try everything else first, then. It sucks to have to make a financial decision when chronic pain is involved. Maybe a chiro will charge you less, though, if you’re paying out of pocket.
Hope you find a solution, chronic pain is no fun.
Just to let you know, you aren’t the only one. That type of pain is one of the biggest complaints I have in my life and that is saying something. I have a massage chair and all kinds of exercise equipment meant to help and it does a little but stops a few hours later. I have often thought that it would feel good to hand myself just because the shoulder tension is so strong is that it would just loosen it a bit.
Let us know if you find a solution. I never believed in chiropractors but I would be willing to try anything that might work.
I think that’s it.
WhyNot is right about the crossed legs, but either posture also causes your back to be at least not quite straight (one leg across the other), sitting in the campfire (or yoga-style) fashion means that your back is arched. Both are bad postures for using a computer. For that you need to be sitting erect, with only the natural arch of your spine (she pontificated, as she realized she was sitting crooked, and abruptly straightened her back). 
It’s entirely too easy to slump, after you’ve been sitting in front of the computer for a while. Then it’s time to get up, do something else for a minute, and sit back down.
I agree with the several suggestions about a chiropractor, with one caveat. I’ve used chiropractors on and off all my life, and there are good ones and bad ones. If you (OP, or anyone else with a similar problem) decide to see one, try to get some word of mouth recommendations. They’re all going to want to do a bunch of X-rays, and you need to make it very plain that you can’t afford all that stuff. One X-ray of your back is necessary, for them to be able to see what (if anything) is mis-aligned. But tell them you want a copy of it (you’re legally entitled). Then, if you decide afterward that you don’t want to go back to that one, you can take the X-ray to the next one.
A good chiropractor can often help with problems like this far more and better than an orthopedist, together with both physical and occupational therapists, sometimes (and would be far cheaper in the long run). But ya gotta get the right one. The odds are that someone who is understanding about your financial situation (in the OP’s case) is going to be a better one, almost automatically.
<soapbox>
Very often, chiros are people who wanted to be an M.D., but didn’t quite have what it took to get into med school. It was once the case that a med school applicant had to show empathy and compassion. Now it’s all GPAs and test scores. That means we get the brightest doctors, but very often, not ones that care the most about patients. After all, in modern America, becoming a doctor is a pretty secure path to wealth, once you’ve paid off the astronomical tuition bills. That attracts more students with the ambition to be financially successful than it does ones who just want to help people. And they (the chiros) didn’t want to be a dentist, or a podiatrist, or something else on that order.
Yes, I know that med schools have finally realized they’ve got a problem in that area, but it was recognized rather late, and - IMO - the correctives are still entirely inadequate. That’s why there are so many doctors who switch from practicing medicine to being writers, or TV commentators, or other things. They never had a vocation for medicine* in the first place; it was just a career choice. 
</soapbox>
*i.e., the overwhelming desire to heal, or to help others
I have a footrest, and it does help. But I can’t comfortably sit for a long time without either one leg tucked under me or both legs folded like in Spectralist’s first picture (guys walk by my office and either admire or heckle me for sitting like this). I’m working on trying to decrease the time I have my knees bent that way, but it’s comfortable for most of the day.
I love posture threads. Seriously.
I’d strongly suggest that your computer posture (duh) is the primary, perhaps sole, cause of your pain. Constant computer use lends itself to slouched posture, continued internal rotation of the arms, tightened shoulders and a hyperextended cervical spine (the chin-out-and-up mentioned earlier in the thread.)
I could conduct a full dissertation on the matter so it might just be best to read this page on postural problems. Here’s a more verbose discussion of the same topic.
Of course your pain might have nothing at all to do with any of the problems found above, but I’d bet it probably does. All a WAG, IANADyet.