flat stopper giving me flats

I was hit by a car the other night. T-boned and knocked me to the ground. Nothing broken on myself or the bike thankfully. Even rode home. But when I got up the next morning my rear tire was flat. Put in a new tube and then on my way home last night I got another flat -- in the same spot on the tube. This time I looked a bit more closely and noticed this crack in my tuffy tire liners. My inner tube had been working its way into this crack and was working a hole in my tube. Cut this piece off, put in a new tube and rode home. No flat today. This seems to be a weird thing to happen to a tuffy liner so I have to wonder if the crash didn't somehow cause this? I was hit in the rear of the bike... probably not but it does seem to be an odd qoinqidinky.

this easy?

So I'm sponsored by a local bike shop and for some reason it doesn't seem to work the way I'd like it to work. Just want to order something and be able to pick it up on my way home. Just need the Rema 16mm patches. Will it work? We'll see. I've send an email. I'm thinking it should be pretty simple but I've heard less than stellar things about how this works with this shop.