Hears feel blocked and hurt and pop when blow constant runny nose. Chesty cough trying to get mucus off chest. Been 10+ days. Likely viral?

Viral or seasonal. allergies can cause all of the above symptoms. You may continue on until your sinuses plug up and get infected. Then you would have to deal with headaches, fevers or fatigue, severe congestion, phlegm, etc.. Hopefully it is a cold/ upper respiratory infection by virus and resolve within the next 3-4 days.
ETD. Sounds like you have some Eustachian Tube Dysfunction leading to the ear discomfort. This probably started off as a viral process but your starting to get to the duration where we'd consider a bacterial infection on top of it. If you're not too sick you could treat symptomatically for a few more days to see if you can shake it and then if not get checked out. Hope you feel better soon!