We don't tag ours until 4 months. That's in August, but we live on a windy hilltop so often not a problem with flies.
Are you keeping the applicator clean between applications? This just needs to be physically clean, as for example wiping over with a baby wipe to make sure there's no blood or tissue from the previous ear.
Once the tags are in, keep a close eye on them, and as soon as you see early signs of irritation then clean up and use the blue spray. Prevention is always better than cure.
Some tags are worse than others for irritating the ear. Small breeds need something soft such as Allflex Bubblegum tags, which are what we have settled for after trying several different types.
Yes, as Foobar says, just take out the old tags, allow the ear to heal, then apply a new pair - after all, you are the only one who knows the lamb had previously been assigned a different number, so what they end up with is what matters.
The exception is if you have registered your lambs, in which case you need to notify your breed society of the change, and enter it in your flock record book.
(cross posted with Marches Farmer)