I have a 97 Contour. It squeaks for maybe 7 or 8 seconds when I first start it. It's coming from inside the motor, haven't listened to see where from yet since it just started a day ago. I had heard it may be a belt. I had the whole timing system changed about 2 months ago but the timing belt is different than the other belts right? Could the squeaking be a belt? I had heard it may be a water pump or alternator, but there is no coolant leaking and the battery is always charged.

Most likely a serpentine belt. Get a can of belt dressing and spray on it while the car is running. If it stops, there's your problem.