Hello Matthew Smyth,
I understand that you want to develop a MATLAB program that can simulate the game of hangman. Particularly, you are facing an issue preventing the same input from being entered twice or stopping the correct-guesses counter from incrementing again for an already verified input.
After inspecting your code, I identified a few areas in the code that can be modified.
-  This if-else block will always execute the else block as the condition can never be true.  
            if incorrectCount==length(guessingWord);
                guessesLeft=guessesLeft-1;
                fprintf('Your letter is not in the word!\n');
                fprintf('You have made a correct guess!\n')
- Consider combining the first guess prompt with the while loop to make the code look cleaner easier to understand.
- The looping conditions seem to be incorrect.
- The second half of the while condition seems to be incorrect even according to your current logic
            while ~(guessesLeft <= 0) || ~(correctCount == length(guessingWord-1))
Coming back to the main issue of mitigating the incrementation of the "correctCount" counter for the same input, a truth-table (boolean array) can be considered. Initially a truth-table of size "guessingWord" could be initialized with all indexes set as false. Once a correct guess is made, that index can be flipped to true so that correctCount" counter is not updated again for that particular guess.
Here is a sample implementation that combines all of the above suggestions
IsGuessed = false(1, length(guessingWord))
while ~(guessesLeft <= 0) || ~(correctCount == length(guessingWord))
    UserGuess=input('Please enter your guess: ','s');
    for i=1:length(guessingWord)
        if (UserGuess==guessingWord(i) && IsGuessed(i) == false)
            lettersLeft=lettersLeft-1;
            correctCount=correctCount+1;       
            incorrectCount=incorrectCount+1;
        fprintf('Your letter is not in the word!\n');
        guessesLeft=guessesLeft-1;
        fprintf('You have made a correct guess!\n');
Again, this is only a sample implementation. Please feel free to make changes to it as per your requirements.
Hope this helps!