There's something about a word needing a concept and concepts needing words that doesn't feel quite right
That would be because, half of your statement, by itself, is incorrect. Concepts in your mind don't need words - unless you wish to communicate the concept.
I've often enough experienced the situation where : there is a concept in my mind that makes perfect sense to me, but communicating it is difficult, either because : the English language doesn't have words that properly explain the concepts I have in mind, or I can't recall the correct word. Of the two, the first difficulty is always the most interesting experience.
In relation to inner dialogue - concepts in your mind, can be modified / changed / clarified by the structure of your inner language (which is an extension of language itself)....remember that the words we use already have associated meanings in our mind...so if we choose to explain a concept using particular words - then all the meanings already associated (in our mind) with those words becomes associated with the concept we were trying to explain (unless of course, some other dialogue runs to counter that)
My personal belief is that : mind affects body and body affects mind. Most people accept that mind affects body...people are less clear on the reverse, yet there are a plethora of examples that show this : muscle memory, smile (even when you don't feel like it) and you feel better, tiredness affects peoples mind (so obvious when you think about it), people love dancing & singing for a reason (and it makes them feel good for a reason - which isn't just related to the body being active), fitness affects peoples ability to concentrate, people undertake 'training' for a reason, etc.
...that's all to point out (back to my first premise of the above paragraph) that not only do our words affect our inner dialogue, but so does every guesture (remember that guestures already have an associated meaning to you)...
...and I'm now of the belief - so does every posture and every motion we make (but that's another story)