What have made you to think that you mum is going into menopause?
Did she start to experience irregular periods?
I don't think her sleeping problems are due to menopause.
Only 1% of women have their last period before the age of 40, and is usually, connected with some other medical problem.
You did the right thing when you suggested her to stop using dayquil, because being nervous, dizzy, or sleepless are side effects of this drug and its use should be stopped.
How is your mum feeling now?
Does she still have sore throat?
Is it accompanied with fever?