You have been given some excellent advice on here , so please please take it. Have been in your position myself almost identical event , at that time I had a GSD as well.
I was worried sick about the event , and my neighbour was a very agressive man.I felt intimidated and rather fearful of the outcome , but went to the police and told them everything that had happened.They were very helpful and told me to inform my neighbour that I had been to see them .I did this as soon as I got home , and I added that unless his agressive behaviour towards me stopped , and that he kept his dog under control I would contact the dog warden about his dog, and i would also seek legal advice about him.
He began to swear and then slammed his door shut.
We have not spoken, since 4 years now , but there were no further problems.
I was absolutely scared stiff of going to the police but am pleased I did because it would have gone on for ever.My dog was also on a lead like yours.
It is a difficult situation , but you are going to need to stand up to them and please don't offer to pay any vets bills.Sincere good luck .Brenda.