Let's take your questions one by one:
Is it possible to use two negative words in the sentence?
Absolutely. For such a sentence to make sense the negatives are commonly of different types (I'm not negative, nor am I wrong), since when they aren't (I'm not not talking to the police officer...) the general feel is that the speaker is trying to be intentionally misleading (I didn't do nothing!) or obtuse (Was it interesting? Well, it wasn't uninteresting...).
Is my use of the two negative words correct here?
It is indeed. The negative conjunction nor ties the dependent clause into the rest of the sentence grammatically. I might suggest putting a comma after appropriately (commonly referred to as the Oxford comma), but the sentence is still correct without it.