"Fit in" is a common phrasal verb, but it means something different from "fit together". Literally, something "fits in" when it connects properly, or matches well with other objects. For example, each of the blocks in this children's toy fits in with the hole made for it:
Figuratively, something or someone "fits in" when they conform to their environment or surroundings. A new student at a school might "fit in" with the other students by dressing similarly, making friends, and/or adopting the same dialect.
The key similarity is that some object is neatly inserted into (or integrated with) another object. You can't do this with two words -- or at least, you'd have to explain what you mean. It's not obvious how one word fits in to another word.
Instead the natural idiom would be to say that two words fit, or fit together, because each fits with the other. It's a balanced relationship. For example, "peanut butter" is a substance with the consistency of butter, but made from peanuts. It's a compound noun that makes sense.