I recommend asking a doctor but if you feel slight relief when you burp then it could be a build up of gas that got stuck and won't come out. I have had that and my grandfather went to hospital because of it not knowing that gas was the cause of the pain. Hope this helps.

Honestly also doesn't sound far off from when muscle spasms in my back or a slipped rib will radiate to where my ribs meet in the back and lead to costochondritis. I'll get this tight sensation like a corset tied too tight and sharp pains in my back. For me at least, it'll usually start to settle down after I load up on magnesium or muscle relaxers and either myself or someone else, like a chiropractor, manually corrects any subluxations contributing to the tension and pain in the area. There's this crack I can get in my back between my shoulder blades, and a lot of times when this is happening, getting that crack to go will sort of unlock the giant knot and I'll be able to stretch out the tightness until it's just sore, but without the sharp stabbing. I know a lot of radiating pain can lead to distress in nearby areas, like when a toothache or tight neck lead to a headache. I've also noticed the pain can go down a bit through belching, but it's different from when my GERD is acting up and I'll frequently have the urge to burp, it feels more like just having less in my stomach puts less pressure on any nearby angry muscles, because I'll get a similar relief from urinating when the muscles in my lower back are in serious spasm, or honestly even from exhaling during these bouts of muscle spasm. It's a feeling like reducing any amount of pressure coming from within my body is helpful simply because there's less to press against the nerves and muscles working overtime.

I would go see a professional, and refrain from doing things that aggravate the back and rib area