Question about shoulder injury from exercise?!

You could be describing tendinitis, or probably a lot of other things too. It sucks not having insurance. A sports doctor would probably be my first call if it was me.

What yoga or body weight have you been doing that involves your shoulder?

This is probably obvious, but stop using your shoulder in any way. Take ibuprofen because it works very well for inflammation.

You’ve ramped up a lot of exercise pretty quickly if you weren’t exercising at all before. Pay attention during you workouts and try to identify if any particular exercise causes more pain. Then stop doing it
It could take a few to several weeks rest for it to resolve on its own if it’s just tendinitis, so give it some time.
First you probably need to see a PCP and physical therapist. If that doesn’t help, you would need to eventually see an orthopedist, who determine if there’s a tear. After a physical exam, they would probably do an MRI without and with contrast. They would tell you whether surgery is necessary and possibly offer you a steroid injection to reduce inflammation and pain.
Wishing you the best.

Understand the difficulty.

The wait time to get into what is considered a specialist, and the fact some require a family Dr to recommend you first means another Dr visit and payment and wait.
The lack of insurance for the now more expensive Doc and original. And perhaps visits to 3rd party for MRI or Xray with wait times and expense. ugh. And no cut rate for paying cash up front.

I'd personally recommend a Sports Physical Therapist in this situation. Not a general PT that may focus on just helping people live and do normal daily routines. You want to get back to exercise, plus the normal stuff.
They generally can't do X-rays or similar which would really add to your expense anyway, and if soft tissue would not always point out something anyway.

And from times that I did have something found by a Dr first - the end result was still a PT, and things for me to do.

Ask local family and friends for recommendations while researching local options. Drive around to some and see how busy they are from parking lot during lunch hour and right after work. Good ones should be busy.
While a PT may want you to come back say 3 x weekly for so many weeks, just to make sure you are doing the recommended treatment and progress changes - not required I've found.
Get all the info up front, starting movements, what would be next, when would it be brought in, how would progress be done.
And how many weeks out to visit to evaluate again?
And then do the treatments.

I've actually been surprised how much good PT stuff is available on youtube now, but shoulder I'd want personal eval because many tests could be needed for where the issue is. But once that's known, I'd bet you'd find exactly the same treatments mentioned on youtube as PT would give you, along with the progress to move to.

Even if the issue is more serious, the PT would likely give a treatment that would not cause more problems - it at least would strengthen the area, and help confirm or narrow down whatever might have be suspected.

Around here it could take 3-4 weeks to get into specialists anyway - that's 3-4 weeks of doing something useful that may end up being all that's needed anyway.
On some things lack of movement isn't helpful. You do need movement. Correct movement.
Like ice is generally only helpful for initial inflammation from whatever caused the issue - weeks later it's not doing much unless you are continuing to cause incidents and inflame it.

Here's some more resources talking about John Kirsch's book (from his website).

https://www.kirschshoulder.com/video