I don't know what is wrong with your shoulder.  EDIT: I see that you injured it doing pushups.  That could be a number of things from a pulled muscle to a torn ligament to a partial subluxation like I had.

A few weeks ago I had a partial dislocation of my right shoulder and it was sure painful! The pain was sharp and intense and always there. In fact the shoulder joint felt "pinched" like it was stuck and wouldn't go in certain directions.  It popped out of place during the night while I was sleeping and then back in a couple nights later while I was sleeping! For the next 3 or 4 days it would pop in and out on it's own, most often while I was sleeping!

I didn't get to the emergency to get it put back into place because it went back in on it's own before I could get there. However dislocations usually require the joint to be looked at and put back into place by a doctor.

Now, since I don't know what is wrong with your shoulder, I will tell you what I did for mine and this is only after the joint was back in place. If the joint is out of place, nothing is going to help the pain until the joint is put back in.

1. Take Ibuprophen.  I buy the generic stuff but something like Advil is the same thing. Follow the directions on the bottle and do not take more than is recommended, or more often than is recommended.

2.  Apply ice packs to the shoulder.  Bags of frozen peas work well, refreeze and reuse as needed.  I use those hard plastic cooler packs that have anti freeze in them and wrap them inside a small towel.  Apply for 20 minutes every hour.

3.  I made myself a sling to wear while I was walking around or laying down or sleeping. I used two nylon straps from my CD carrying case that I snapped together for when I was at home. When I went out I made a nicer one out of a silk scarf :)  No need to get fancy.  Just put it around your neck like a long necklace and then put your  forearm into the lower part so it is at a 90 degree angle and it doesn't hang down. This takes the weight off of the shoulder  joint.  When I was in bed I kept it on in order to prevent the shoulder from falling backwards. This really helped! It also helps to have a pillow behind your shoulder to support it and keep it aligned.

4. I avoided certain movements with my arm that contribute to the type of dislocation that I had. IE: lifting my arm up beyond level with my shoulder;  moving my shoulder backwards.  In fact I tried not to move the part of my arm between my shoulder and elbow at all. I tried to keep it close to my body and just move the part of my arm from the elbow down.

That being said, even those without insurance are entitled to healthcare.  There must be clinics in your area that you can go to?!

"It is good to see ourselves as others see us. Try as we may, we are never
able to know ourselves fully as we are, especially the evil side of us.
This we can do only if we are not angry with our critics but will take in good
heart whatever they might have to say." - Ghandi