This could be anxiety, but I would talk to your doctor about it.
I had the same thing. It got worse when I had a cold and I assumed I was getting pneumonia as I'd had it before. I'd also been in a car accident and talked to my chiropractor about it thinking something was out of whack.
All tests came back negative.
Long story short, I ended up breaking out with shingles. My pain actually started in my back but the first little bubble appeared on my chest between my breasts. It was then they knew exactly what it was.
I don't want to scare you because it's already making you nervous, but my pain was so bad, taking my breath away, that I told my mom I feared I had a lung tumor or something because it was just becoming increasing difficult to breathe and the pain was unbearable.
Get checked out by your doctor. Have you had chicken pox? If so, you can get shingles. They might be able to give you an antiviral to lessen your symptoms. Talk to your doctor about the shingles vaccine.
I'm not a doctor, but this painful intermittent nagging pain and squishing that you are describing sounds like what I felt for quite a while before I actually broke out.
Since I've had shingles, I know the signs and I can get medicine when I feel a flare up such as getting a cold sore. I know the virus is active in my body.
It's manageable.
I can't say whether or not this is what is causing it, but your symptoms merit a visit to the doctor for peace of mind, if nothing else.
Very best wishes. Take care.