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There are a lot of variables here, as various ones have mentioned. Boxing out can be legal or illegal, moving screens aren't always illegal, and none of that has anything to do with the key. Perhaps you could re-describe the situation? Who got where first? Did you have legal position? Did your opponent? Was verticality an issue in the play? Was there contact?
Your play-pic is very good, and helps way more than some of the other questions we get, but it would be even more helpful if you could describe how the play unfolded over time, and use A1 to mean the shooter, A2 to mean you, and B1 to mean the defense who claims you "moving screened" him.
Example: A1 and A2 crossed the division line at the same time. B1 was near the top of the key intending to guard A1. A2 ran ahead and set a screen to keep B1 from the shooter. A2 established legal position so that A1 could get to the basket before B1. B1 attempted to get around A2, but A2 moved to keep B1 away from A1. B1 pulled up and there was no contact.
In this play, the description tells each action and how the players were relating to each other. If you can describe your play like this we can give you some guidelines that might help you determine how to do things legally next time.
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