Both words can be used for similar things, but there might be a slight difference with the emotion attached to the words.
Squeaked = sometimes a shorter, high-pitched noise, can be used for somebody who is frightened
(She let out a squeak when she saw the spider.)
Squealed = sometimes a longer, high-pitched noise, can be used for somebody who is experiencing distress
(The pig squealed as it ran away from the fox.)
It's a little tricky...they are similar enough that it can be used to describe a lot of high-pitched noises but certain phrases use each word more often.
e.g. a mouse squeaks, a door or floorboard squeaks
a pig squeals, a car tire can squeal
Sorry, I hope that helps a bit.