There are allergies that are associated with back pain, but most present with complaints of "lower" back pain with this. Pollen, bee stings, eggs, milk, shellfish, etc. are common with this symtom.
There are many, various conditions that may also cause these symptoms of "rib pain". Common of which muscle strains, sprains or tears between the ribs or along the back will portray as the actual ribs hurting. Because your pain is constant, and worsens as the day goes on, this may also be related to the lungs. When the posterior part of the lungs are infected and/or affected (this may also include tissues surrounding the lungs) will feel like the ribs are hurting. Certain types of viruses or bacterial infections may also cause these symptoms. I would suggest taking an OTC NSAID (non-steroidal anti inflammatory drug) analgesic such as Ibuprofen, Aleve or Aspirin to help alleviate the pain, and also would recommend that you make an appointment to see your primary care physician when possible. He/ she may obtain x-rays and further testing (blood studies) to rule out allergies, lung, bone related issues and others. Because of the various conditions that may cause this type of pain, it is difficult to specifically determine your diagnosis. Treatment will ofcourse depend on the diagnosis, but early detection and treatment is key. Some conditions concerning the lungs may develop into more serious complications if left untreated. So I would suggest that you see your MD when possible for further studies.
I wish you the very best!
If you have any further questions or concerns, please do not hesitate to ask.