Can you get sore glands from chronic post nasal drip?

No, not usually.: Glands will swell for weeks after an upper respiratory infection, which causes drainage (briefly), but you said "chronic". I noticed gastritis and Prilosec on your profile. Are you sure post nasal drip isn't from GERD? Happens a lot. But look for other reasons for cervical gland pain or swelling. See your primary care, make sure your glands aren't a sign of something serious.