I'm not sure that it is actually necessary to distinguish between inflection and derivation just for the sake of it, but if you are pressed to do so for some reason I suppose you could apply the usual shibboleths.
If this affixation is a lexical operation (building new words in the lexicon), it's derivational; if it's a morphosyntactic operation (constructing sentences from the lexicon), it's inflectional. If that distinction feels like unempirical theory-mongering, you're appreciating why djr33 and I are reluctant to give a simple answer. If the distinction between derivation and inflection isn't consequential in some way, you may as well be counting angels on pinheads.
In my work, I (like many others) make a distinction between inflection and derivation in terms of productive regularity and semantic predictability. This is important because I am interested in language as a socially shared system of knowledge. In those terms (and off the top of my head), the language you're describing looks relatively polysynthetic. I have a hard time imagining in useful terms that speakers of polysynthetic languages are inventing novel lexical forms every time they utter a sentence-word, so I would tend to call that kind of thing inflectional.
