Yes it does seem like leaf miner, but without seeing a picture I can't be positive. Could possibly be fungal but I doubt it. There are two leaf miners for Holly. Native Holly leaf minor and Holly leaf minor. They can both treated when they are in the adult fly stage. Conserve (a very low toxicity pesticide),Orthene, or Merit will control these pests. Malathion will not.
If you are willing to time your application then Conserve will give you good control. The two different leaf miners have slightly different timing. You should take or mail some leaves to your Agricultural Extension service, they can tell you if and which problem you have and the correct timing for where you live. If you are sure you have leaf miner you can take the shotgun approach and treat the soil with Merit (Imidicloprid) as soon as the soil is workable.
I try to limit my Merit use to only where nothing else works because of its possible link to Bee mortality.
BTW. Meserveae are listed as resistant to leaf miner.

So confusing, BUT THANK YOU SO SO MUCH!! Meserveae reistant to leaf miner? But resistent doesn't mean completely immune to...I guess..

I studied so thoroughly photos of leaf minors in hollies, and nothing looks like this...

I Hate all "chemical treatments" as I fear for the earthworms, which the birds eat, the bees, everything...

I never knew I could mail leaves to the local Agricultural Extension, that's great!!! Do they charge you? THANKS SOO MUCH FOR YOUR FEEDBACK!!!! With everything!!!

Oh, I too ruled out fungal..
Amy

I Don't know how much they charge, mine charges around $15.
Call them first and get instructions on how to take samples.
I don't know where yours is, usually they are part of the state university. Conserve (spinosad) is gentle on bees and other predators. The label says it is only toxic to bees for three hours after application. If you treat late in the day after the bees are home you should be safe.
As a note to all, Your Agricultural Extension Service,(or Cooperative extension) is a great and under appreciated recourse. Try to drop a note to the Governor and Legislators when they help you out as they are always under the budget axe.

If what you have is leaf miners there is really no pesticide that will be effective against the larva inside the leaf. Some pesticides may be effectgive against the adults and keep them from laying the eggs that become the miners.
As a rule leaf miner damage is more cosmetic then harmful.

Actually Merit in the soil will absolutely control Both Holly and Native Holly Leaf Miner, it translocates into the leaves and will give excellent control. Orthene though technically not a systemic but a penetrant will also give control. Conserve as stated has to be sprayed for adults. Kimmsr is right about the Leaf Miner not being that damaging, and Hollies can handle them but some people don't like to see their Hollies loose most of their leaves. Of course we still have not established that this is Leaf Miner so we wait for test results before taking any action.

Amy, call your local extension office to find out how to collect your specimens, how to pack it, and where to send it. They may want you to bring the package to their office so that they can send it. Yes, there will be a fee.

You might also ask if it is possible for them to do and ID via some good images. You might be able to email pictures directly for inspection. The images have to be good ones, though. Blurry cell phone pictures won't cut it. ;-)