After practicing on the clarinet, when you push air through your instrument, especially in the extreme range and on a new reed, your instrument may squeak, but not because of bad technique (your tones are clear and precise otherwise). When this happens you should get a harder reed, and if you can't get harder reeds (your already on a 4) then you could think about a larger mouth piece (they come in 7 sizes and 1-3 is for beginners, 4-5 for intermediate and 6 and 7 for professionals.
(edit)
When you decide that you want/need a harder reed, I would highly recommend that, instead of jumping straight from a 3 to a 4, you go for the middle and get 3
1/
2 reeds instead. 4's are immensely stronger than 3's and the likelihood of a person being able to make that jump is slim to none.
(/edit)