Take it to small claims court. You've got a 50-50 shot. Here's why. Dog bite cases generally are strict liability, meaning that you would not have to prove liability. However, the limited defenses that are available to the offending dog owner include provocation and "trespass". Technically your dog was in trespass. Before you scream at the computer screen, you would certainly have the right to go to the door during reasonable hours and in a reasonable manner make a request for the return of borrowed property. However, after that the facts and application of the law to the facts become more complex in that you allowed your dog to follow you across the street. This was not a necessary act in order to retrieve the borrowed property, and so it could arguably be defended that the neighbor's dog, on it's own turf, was defending its propery against a trespass.
Thank your lucky stars that no person was hurt and that the worst of your damages according to your posting was the cost of a prescription.
Keep on the neighbor with 30 day demands, certified, and consider small claims court with the above in mind.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
I agree with my colleague. The cost of antibiotics is quite small in comparison to the amount of time and money you will expend in trying to be "right", which, by the way, you are not. Your dog went on to their property, unrestrained by you, and their dog was on its own property, defending its owners. This is not a battle you will win.
Let it go.