Was the mic ever dropped or did you buy it used?
For some reason, I just can't stop laughing at this even though it's not meant to be funny ! I'm not being cruel, it just tweaked my odd sense of humour.
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All the while that I've recorded, I've made use of varispeed. Like, if I or whoever was singing couldn't reach some notes comfortably, I'd slow the recording down, sometimes as slow as three semitones {say, from C to A}. Of course when put back to normal speed, the vocal would sound half way to Mickey Mouse. Sometimes, by taking some treble {highs} off, that effect of a childlike voice or a high pitched Dylanesque whine can be muted somewhat. The other thing I used to do was double track, but one vocal would be done slowed down a semitone, while the other would be done sped up a semitone. When crunched together {with some EQ~ing and whatnot} it could be quite effective.
Of course, the way you mix your song and the way the instruments envelop the vocal can also have a bearing on whether you sound squeaky. But you may find that the voice you have is the voice you have and unless you disguise it by actually sounding unlike you, that's it. You're stuck with it so get used to it. You may not like it but everyone else might.
