First of all: don't worry.
The constant eye contact etc. Is just some instinctive reaction, as the dog most likely isn't sure on why the whole thing happened. As mentioned in the other reply, stay calm and continue as usual. As soon as the dog realizes it's no longer happening this should change again.
Next time, try to be a bit more careful and "worst case" just let the tick be. Depending on your location, there might be a rather slim chance for any diseases to transfer and damaging (e.g. pressure) the tick might be far worse than just letting it continue until it drops off on its own (as it would act like a syringe).
One of our Huskies - 6 years now - is very trustful, allows us to remove ticks even from next to his eyes, etc. But if there's a bit of redness around one he'd still run from us as soon as he notices what we're trying to do. He'd continue doing so until he notices we've given up.
As for your puppy: sometimes distractions work very well, but this friends on a dog by dog basis. Make the fearful event into something exciting.
For example, try to feed small treats while a second person tries to remove a tick from the dog's back. It's not that unlikely for the dog to make a connection: "If I feel a tick and show it, I'll get stuff!" It sounds weird, but it definitely works.
Our dog I mentioned earlier even has a tendency to force us into cuddling so we notice ticks.
And just to mention it, just in case:
If you haven't done so, get a tick hook or tick twister (marketed under many different names by different brands), if you're still using tongs or just finger nails! Far easier to use and a lot less likely to accidently hurt the dog.