I have done the alamycin injection but it needs a
very fine needle, which you likely don't have to hand.
Before going to those lengths - do you pinch the eyelid when you turn it back out? Just bruises it enough to cause the slightest of swellings, and is often enough to keep it from inverting again
Another thing... ime, this occuring can be an indicator of dehydration, and when it's an older lamb like this, sometimes coupled with mastitis starting in the ewe, so it's a good idea to also check if the lamb is nice and full and the ewe's udder is as it should be.