Hey this is one of my first puzzles and so I'm not sure if it is 'cooked' or unsound. I am still proud of it nonetheless.

 White's first move is positional rather than aggresive. See the move list for permutations. 

 

Feel free to offer me other suggestions on improvements or mistakes,

 Thanks

The quickest mate is Bxf7+ Kh8 (forced as Kf8 leads to Qb4 mate), QxBd3 now threatens mate at h7, if black blocks with g6 then Qd4 is the new mating square and both threats can't be answered. Mate in three, your variation was mate in 4.

Well about half of my variations were mate in 3, but thanks for feedback

Nope, I can't see a forced mate in three if the first of the three moves is Qf4, the only mate in three I see is the one I posted. You can't say it's a mate in three or four unless you opponent is playing the best move available.

So to answer the question, yes it is sound but assuming your opponent plays the best move it's not the quickest mate, I would not play that move in that position.

Have you looked at the variations? - click the 'move list' button. Admittedly your move is a forced mate in three, but Qf4 still creates a situation in which every possible response by black leads to mate: 

1.Qf4 g6 2.Qxf7+ Kh8 3.Qxh7#

1.Qf4 h6 2.Rb8+ Rxb8 3.Qxb8#

1.Qf4 Rf8 2.Rb8 Bc4 3.Bxc4 g6 4.Qxf7+ Kh8 5.Qxh7#

1.Qf4 Rf8 2.Rb8 g6 3.Qxf7+ Kh8 4.Qxh7#

1.Qf4 Rf8 2.Rb8 h6 3.Qxf7+ Kh8 4.Qxf8#

1.Qf4 h6 2.Rb8+ Rxb8 3.Qxb8#

1.Qf4 Bxb1 2.Qxf7+ Kh8 3.Qg8+ Rxg8 4.Nf7#

1.Qf4 Bc4 2.Rb8+ Rxb8 3.Qxb8#

I understand your criticism. Maybe I should alter the puzzle because the thing I was most proud of was the position after Qf4 - no escape for black, and the difficulty I had was making a situation in a puzzle style where white had to see how to get into this position.

TPman: Your puzzle is better than you give it credit for.

Qf4 Rf8 Qxf7+! Rxf7 Rb8#

So there are only two "problems" remaining: First that best defense by black is a mate in 4, and second that even if you fixed that to be mate in 3 that there is another (inelegant) solution to mate in 3 as pointed out by the first poster.

I did see the variations, and blacks best response in BxRb1 hence why it's mate in 4. The puzzle is good however with a black pawn on c4 it would be perfect as Qf4 rather then Bxf7+ is then the best move!

Hey thanks everyone I didn't mean to be argumentative and I will take the feedback into account. 

petershaby: How does black pawn on c4 fix this?

Well it's not a perfect puzzle and not a perfect fix! The pawn on c4 means that the best move is now Qf4 rather then Bxf7 (this was the idea of the puzzle, to make Qf4 the best move) from Qf4 mate is forced

Qf4 BxRb1 (to prevent Rb8 forcing mate)

Qxf7+ Kh8 (forced)

Ne6 (threatens mate) Rg8 (forced to cover the mating square)

BxBb1 All black pawn moves lead to mate in two for white.

So the title of the puzzle can be "White to move and mate in 6" with three possible solutions (The key being Qf4)! 

Sorry I know it's not great was the best I could think up quickly!