I would strongly recommend going to see your primary care doctor
about this issue as soon as you can. It is hard to give a clear diagnosis from the information provided in your question, but it certainly sounds like the symptoms are severe and persistent, and therefore require medical evaluation.
Since you have been going to the gym, overuse or strain of the muscles is certainly a possibility. Strained or pulled muscles often have an aching feeling and they may be sore when you touch them.
On the other hand, the fact that you are describing the pain as sometimes shooting and radiating down the shoulders into the forearms suggests that this might be nerve pain. Nerve pain is often caused by arthritis
or a slipped disc in the neck region of the spinal cord. Other symptoms might include weakness in the hands, or numbness
and tingling in the skin of the arms.
Your doctor will be able to perform an examination and help you figure out what is going on. If this is just muscle pain, they can give you some recommendations on how long you should rest before returning to the gym and on what pain medications to take. If this is nerve pain, they may want to order some additional radiology studies of the spine.