Hi
Welcome to the forum!
Chest pains that are not related to breathing and are very severe can be due to angina, heart attack, aortic dissection and endocardiits. All conditions are serious. The pain can also be due to severe gastritis, acidity and GERD but not severe enough to give a ripping sensation. The other possibility is thoracic outlet syndrome, which happens due to compression of nerves or blood vessels, or both between the base of the neck and the armpit (thoracic outlet).
I would strongly recommend you to consult your doctor ASAP, maybe go to the ER. It is difficult to comment beyond this at this stage. Please let me know if there is any thing else and do keep me posted. Take care!
You should go in to make sure it is just musculoskeletal in nature and not something far more serious. The pressure feeling and ripping feeling sound serious enough to warrant a doctor visit!