Are the following sentences acceptable?
1. In today’s society, each person might be under pressure in some ways, such as schoolwork, work, and family.
2. Some people’s slumber might be influenced because of being under too much pressure, so it will bring out insomnia.
As I said, I underlined the parts which had a problem. We don't use "because of" after "influenced", we use a 2-letter preposition.
And we don't refer to insomnia as being "brought out". There is another phrasal verb which would work there which starts with "bring" and is followed by another 2-letter preposition.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
For the other part of the sentence, the similar thing I can find in my favourite dictionary is:
bring something on:
to make something develop, usually something unpleasant
eg He was suffering from stress brought on by overwork.