Yes, all of this could be related. If you swallow the gunk from your sinuses, then yes, that can upset your stomach.
Also, your body is all linked anyway. The fact that you have back pain too is not uncommon and is to do with the nerve pathways throughout the body. The main nerve the Vagus nerve causes a lot of stomach and bowel problems, as this runs from your head all through to your belly. There are also nerves around your back that run around the line of your belly and can cause belly pain and back pain at the same time.
You have to remember though that everything in your body is connected and interrelated and it functions as a system, so unfortunately, no one symptom in the body can ever be taken in isolation.