Be happy

Late in the afternoon, one of my classmates came back from her home and she was deeply hurt by his her boyfriend.

"came back from her home" isn't incorrect, but it sounds strange because you didn't tell us where she was going. This sentence implies she was at Place-A, then went home, and then went back to Place-A.
Is there another way you could say this? Perhaps tell us where she went instead of where she came from? For example: "One of my classmates came to my house" "came to the diner", etc.

I pain her a lot, but actually, I know that we girls must be independent and don't not rely on others.

If you split your "I know that we..." part into two sentences, it would be "We girls must be independent. We must not rely on others." Therefore, "do" is unnecessary. If you are trying to say "we don't rely on others" as reason for needing to be independent, then change "and" to "so" or "therefore".
'We must be independent, so we don't rely on others.'

"I pain her a lot"
implies that you hurt her feelings.
"I bother/annoy/give her trouble" I think is better in this case.
As a reader, I'm a little confused as to why you bother her.
If you choose to write a reason, you could say "I bother her because I __reason_here__, but actually, I know..."

We should not allow others to dominate our life and feelings.

It seems everything has changed, but... whatever. Tomorrow is another day.

Your sentence is pretty colloquial. If you want to keep that colloquial feeling, then this is how I would personally express it.
If you were writing this sentence in something formal, this would be an acceptable way to express it:
"It seems everything has changed, but it doesn't matter. Tomorrow is another day."

Also, a note about though and but. A sentence can't use both of them. You should either say, "Though it seems everything has changed" OR "It seems everything has changed, but"