I didn't want to mention a specific store, but yes, the walmart pharmacy section was where I found them, I didn't have to ask the pharmacist, it was right out for sale in the open along with things like earplugs. I am guessing the pharmacist you spoke with was just a blithering idiot.
I don't see why it would be banned anywhere, there is no needle or way to screw one on, it's just a method of accurately measuring liquid medication for oral or topical use.
I am sorry I threw away the original packaging, but here is a picture of mine:
I did a google search on Oral Medication Syringe, and there are several manufacturers, but the one I bought is made by Apex. Here is an Amazon link to a 3-pack:
Amazon.com: Apex Oral Medication Syringe, Small, 1 syringe (Pack of 3): Health & Personal Care
But try some other pharmacies first. I lived in NJ for a few years, and it seemed less restrictive than IL is. Call places and ask first. Call multiple times at different hours so you are asking different people. Make sure you are very descriptive. You could say it is used for giving something like cold medicine to your elderly relative, and that it is also used to measure medicine for children.
This is just my opinion: Remember that any place you call, from a top-of-the-line engineering firm to a local pharmacy to a grocery store, the first person you get to talk to is often the person who is barely keeping their head above water and needs to be baby-stepped through anything. The competent people are usually busy doing the actual work. Be patient until you get to talk to one of them.