Your baby is young, to be "sleeping through the night." Sleeping through the night, for a baby, means sleeping for at least 6 hour stretches. But this comes in time. My kids, did not sleep through the night, until they were about 2 years old, consistently. In between that, they had periods of sleeping for longer or shorter stretches, but it changed per their development and hitting milestones and teething, and night-terrors etc. All "normal" things which they go through.
the squealing is a developmental thing, as they "discover" their voice. And yes, it can be ear-piercing. UNLESS, when she is doing it she seems in distress or in pain... then I would consider another cause for it.
Its a phase. One of many. Each child being different.
Are you still feeding her on demand? She is waking, and she could possibly just be hungry... at this age, they are approaching a 'growth-spurt' and then, they need more intake and get hungrier, more often. BOTH my kids did that at growth spurt periods. If they are hungry, a baby can't sleep. Try giving her a good feeding before bedtime, and cluster feed her... which means, that sometimes a baby, when growing, will often even need to feed every hour. Go according to HER cues... a baby has no other way to communicate "hunger" because they can't talk yet, and so they wake... or scream.
Both my kids went through periods when they woke more often at night, because they were growing and needed more intake. I fed them on demand, for the 1st year.
For the 1st year of life, per our Pediatrician, a baby should be fed on demand. So that, when they are having growth spurts especially, their intake needs are keeping up WITH them and their natural growth and development. At times like this, feeding on a "schedule" will not work.
ALSO, when a baby is hitting milestones and "changing" developmentally, they also tend to wake more. It's "growing pains" for the baby too... and they can't help it. Especially when so young, as your baby, they can't do things at-will, yet.
For me, when I had my 2nd child and he woke/cried at night... it did not wake up my daughter... because for some reason, she said that she knows it's just her brother and so "its okay...." and it didn't bother her. She understood that babies wake up and cry at night and they can't help it. She sleeps through it all.
You can try and check about her reflux as well. BUT, for babies, their sleep patterns are not "static" and they change all the time and so rapidly and it puts a kink in their ability to sleep.
Sometimes, if a baby/child is "over-tired" or over stimulated, it also makes it hard for them to sleep. They need to nap as well, as this helps them. Does your baby nap?
Well just some thoughts... hope this helps,
Susan