All I know is that if your timing belt chain whatever slips then it is going to cost thousands.

The squeeky noise you hear is most likely the alternator sliping on the serpentine belt. This is especially true right after start up because the starter just put a huge drain on the battery and the alternator works the hardest to top it back up. You probably also need a belt tensioner unless the belt is obviously bad.

John Roncallo