HI JJ. This is a very common injury when you first start to invert. The most likely cause is improper form and/or muscles not being strong enough for the move. The move should be controlled, without any kicks. Your body should be in front of and up against the pole to avoid "smacking" the pole with your ribs as you go up, which is most likely what happened. Even though you can get yourself up there, it sounds like your body wan't really ready. Super common for eager polers!
If you do not have Veena's lessons, it would be a very good investment to do so. She explains what muscles should be used, and proper technique through the entire move so you can avoid injury.
If you are having trouble beathing, then you should probably see a doctor. There are several different injuries that can occur. Bruised bones and pulled muscles are most common. At the very least, rest as much as you can, ice the area, and if your stomach can tolerate it take a anti-inflammatory. There are lots of good homeopathic treatments out there as well.
Since you are just starting, now would be a good time to get into the best habits to avoiding injury by making sure you condition your body for a move before you attempt it. I wish someone had given me that advise when I first started! If you follow Veena's lessons you will have the best chance of doing that.
Welcome to the wonderful world of pole!!