This is common.
YOu have been lucky that your baby has been a good sleeper since birth. THAT is unusual and not common.
So her waking at 3:00am is naturally not easy.
But actually, waking only at 3:00am is NOT that bad.
She is after-all, STILL sleeping through the night and doing at least 8 hour stretches of sleep, still. So that IS good.
But because she is waking "screaming" as you say, to me, indicates either "Night Terrors" or teething. Which both can crop up at about this age. Or, sometimes it is illness.
Or, sometimes, at certain age-junctures, their REM sleep patterns change too, and gets tweaked. And nothing we do, can change it or stop it, because it is developmental based.
As far as your concern that you might create a "bad" habit in order to get her back to sleep... I don't think so. And if a baby needs help to sleep, they need help. Because if after an HOUR of her not being able to do it herself, to me means she needs help.
BUT, there seems to be a pattern of her "screaming" awake... then intermittently crying off and on for about an hour, and "not" being able to fall back asleep on her own. Well, sometimes kids do that. Both my kids had moments like that too. But I observed them and their eyes would still be "sleepy" or closed... they were NOT "wide awake." So per those cues, I did not "wake" them more. I just kept quiet, patted them/rubbed their back and soothed them... would tell them verbally "Mommy is here..." and just hearing my voice they felt comforted and would go back to sleep. But it take patience. On my part. My daughter, would even "wake" but still be actually sleeping...and would even sometimes sleep-walk.
Their REM cycles gets affected sometimes.
Or, sometimes it is because they are over-tired or stressed and then their sleep gets affected. And also, at various ages, they can start to get sort of "night mares" too.
For my son, when he was about 1 year old, he had 'night terrors.' Then that phase stopped. As I knew it would. And then, once in awhile, he'd get night-mares. And he would even talk in his sleep or yell and what not. BUT, he was actually still asleep, but a little conscious and could hear me and respond back. But at these moments... I did NOT "wake" my kids... I just let the pattern occur... naturally. And the phase would stop. So, I did not "interfere" with it or try and wake them and "talk them out of it" or try and reason with them. I let them be, but soothed them like a stealth jet. No lights were put on, just kept dark and quiet.
I know, it's not easy, since your daughter has been such a good sleeper all this time.
All the best,
Susan