I get "None" at the end of my printed result.

[ThomasL]

You are assigning "check" the outcome of your function str_analysis()
and the default value of return is None.
So "print(check)" prints "None".

Better pythonic way:
Don´t use print() inside a function that is doing something.
Always return the value of the outcome of this "doing".

def str_analysis(your_input):
        if your_input.isdigit():
            if int(your_input) > 99:
                return "Big number"
            elif int(your_input) <= 99:
                return "Small number"
            else:
                pass
        elif your_input.isalpha():
            return "Your message is all Alpha characters"
        else:
            return "Your message is neither all Alpha nor all Digits"