I nursed both of my children for way over a year each, so I am familiar with clogged milk ducts. I stopped nursing about 3 years ago, and twice in the past few months I have gotten what feels like a clogged duct. It feels like it is directly under my aureola and on the underside of my breast. I know I should get it checked out probably but there is a long waiting list to get in at the clinic. I can't find anything online for non nursing mothers. Is this even possible if I am not producing milk?

Yes, it is possible... even more so because you have breastfed in the past. Anyone can develop clogged milk ducts/cysts... they are just more associated with regard to breastfeeding. Do be sure to have it checked by your doctor since there can be a number of reasons for breast lumps.

You do need see a doctor but you can slightly massage in a warm shower like you would if you were nursing. Even if it clears up you still need to see the doctor.