If the expected delay at today's destination would have been more than 1 hour, then, according to EU Regulation 1371/2007 article 16, you have 3 options, one of them being: "continuation or re-routing, under comparable transport conditions, to the final destination at a later date at the passenger’s convenience.”
That means the local operator (= DB) should make your ticket valid for your chosen date at no additional costs. I don't know how that works in practice with an Interrail pass (I can image some ways, such as issuing a 0 EUR ticket), so you'll have to ask the local staff. Do allow enough time for that.
Did the the local staff advise anything?