It's quite hard to verify the differences in meaning between the sentences above because "estar inquieto/preocupado" shouldn't be a constant in someone's life . But I'm gonna try to use two other sentences as an example.
"Estoy inquieto por el examen"
"Estoy preocupado por el examen"
In the first one you are anxious about your test, it wasn't really hard/you now you knew the answers for most of the questions/etc. so you are not worried to fail, however you don't know for sure and you would like to now your grade as soon as possible.
On the second one, you are definitly worried. Either the test was really hard o your final note depens on it.
"Inquieto" however could mean more things like "misbehaving" as the others have answered