Proving NP hardness in Puzzle with SAT reduction
As far as I can tell, no, you have not proved NP-hardness of your puzzle. NP-hardness is precisely defined. If you want to prove a mathematical statement, you must do mathematical work and can't get there by only hope and intuition.

If you want to show that problem X is hard by a polynomial-time reduction from 3-SAT, you should proceed as follows. Take any arbitrary instance $I$ of 3-SAT and construct, in polynomial-time, an instance $I'$ of X. Once you've done this, prove that $I$ has a solution if and only if $I'$ has a solution. This is the "mathematical part", where you use the properties of $I$ and $I'$ to argue for both implications; you need some insight and practice in writing mathematical proofs, where in the argument the next step follows from the previous.

For example, contrary to what you seem to say, you can't show hardness by reducing one fixed instance of 3-SAT to your problem X.

If all this feels confusing but you are still excited, I recommend that you:


Read the relevant definitions of NP, NP-hardness and polynomial-time reductions. Think about what they mean intuitively as well.
Look at examples of reductions and NP-completeness proofs. Don't expect to get it straight away, but be willing to do some work. There are plenty of exercises out there and many questions on this site too.
Come back to your original problem later, perhaps after getting a little bit more familiar with writing proofs in general.