Wow, am I glad I popped into this question. I am really interested in the product B posted a link to, going to order some for my pack!
In the meantime, WW, if you are waiting for your order to arrive, there are 2 fly sprays we use on our dogs that work well, & you can pick them up at a local farm supply store (Fleetfarm, Tractor Supply, etc.). Both sprays work against flies, mosquitos & ticks.
The first is Bronco Fly spray by Farnam. It is approved for dogs (be careful, not all horse fly sprays are!). A spray bottle retails around here for $6-7, we apply directly to the dogs coat when they go outside. You can also use it to spray the permitter in the yard, or camping/other outdoor activities.
The second is Ultrashield Green by Absorbine. It is an eco-formulation with essential oils, & is used the same way as the Bronco spray - direct to coat, or to the environment. Definitely pricier - $20 for a spray bottle (I use this one directly on my dogs, & the Bronco for in the yard & when we travel for dog events).
One other thing - sometimes dogs can react to other things in the environment, & it mimics bug bites (localized swelling under the fur). This is called urticaria, & is most noticeable with short-haired dogs, & I've had 2 with issues when they were pups, that they grew out of. Mosquito/fly bites will be random bumps on the body, but a reaction will have bumps from head to tail, more than you can count.
If that is the case, talk with your vet, as you might need antihistamines. We got prescriptions for Hydroxyzine, it was stronger than Benadryl, & had the added bonus of making our puppies drowsy, so they weren't as miserable.
Hope your puppy is bite-free soon! T. :)