Yes, you need to get the lambs onto the cow-teat side. It'll go back to near-normal size after a day or two of being suckled.
For future reference, we always get them in a pen when they're like this. Milk some colostrum off the cow-teat side for the freezer, and to reduce the size of the teat, then get the lambs on sucking that side. Repeat each feed until it's normal size and you are sure at least one lamb is sucking the cow-teat.
Mark the ewe. Either cull if you don't want the extra work, or know that she'll be donating to the frozen colostrum store again next year
I hadn't heard the trick with the sticking plaster on the normal-teat side. You'd have to be careful you didn't cause mastitis that side, of course, so you'd need to let them onto that teat at least two or three times a day, but otherwise it's not a bad idea.