The chest and abdominal wall muscles are tightening in response to some type of tension that is likely anxiety/depression related. It can be brought on by medication and physical changes before you feel emotional changes. I had spiking heart rates all my life over everything even when calm until I did a complete overhaul of my meds and suddenly I had these weird chest to rib sensations still when my heart rate was fine. I found the change in medication was increasing awareness of existing muscle tension and causing that pressure or sinking feeling periodically. At the most extreme it even clamped down my stomach so food wouldn't process or go out so food didn't want to go in.
It often actually bothers me when I'd go to relax. I read the reason for it but can't remember the details. Overall the body displays a stress reaction after the stress is gone and it is releasing hormones to recover. Unfortunately it then often brings back memories of the cause of recent anxiety or depression and creates a cycle that can lead to randomly crying and being depressed (happened to me a lot when starting to relax for bed until med changes and I didn't understand it then) or even cause panic attacks in some people after nothing is going on around them anymore. During a moment of stress it makes sense but other times the body is just doing a crappy job of cleaning house and going to a doctor will just get you labelled a hypochondriac. Reduce stimulation like light and sound except tolerable distractions-foreign tv I have to read subtitles on works great because you can't stop to think even as much as you can a book but you aren't trying to process anything in life that impacts you like online conversations would, drink some mild liquid-hot or cold depends on the individual but it would instantly improve my breathing for a short period to take a drink, applying heat (that container of tea I've already got now works) to your chest may improve breathing over longer periods, and as hard as it is try not to obsess about it or the thoughts it brings and the changes will pass so you can continue recovering. Sometimes if I was getting ready to sleep when it happened it would help to actually get up and go do some light tasks around the house and things like refilling the chinchilla water bottles even if they weren't that empty yet until it passed and I forgot about it. If nothing is going on then the body is trying to relax but it got stuck switching states and you just have to not make it worse. Now in the moment you've got an entirely different situation to try to counter.
My greatest point is my persistence.