There is no need for a comma after events, since you don’t have to use one before ‘and.’

Also, put an apostrophe after ‘beings,’ since you use it in the plural possessive form.

It’s a good sentence, and doesn’t need to be broken down into two smaller ones.

“Horoscopes are a part of astrology, which is the belief that the stars and other celestial bodies have an influence on human beings’ interactions, events and personalities.”

Horoscopes are a part of astrology, which is the belief that the stars and other celestial bodies have an influence on human beings’ interactions, events, and personalities.

Another option is:

Astrology is the belief that stars and other celestial bodies have an influence on human beings, their interactions, events, and personalities. Horoscopes are an integral part of astrology.

I like the second option better. However, that is a personal preference. If you do not want two sentences, use a comma to make your sentence easier to read.

However, it might be better to break that into two sentences:

Astrology is the belief that the stars and other celestial bodies have an influence on human beings interactions, events, and personalities. Horoscopes are predictions about the future based on astrology.

I agree with your English teacher. Among their many functions in English, commas set off nonessential phrases, clauses, and words, so I would put a comma after astrology because I don’t absolutely have to know the description of it to get the point that horoscopes are a part of it.

Why?

Use a pair of commas in the middle of a sentence to set off clauses, phrases, and words that are not essential to the meaning of the sentence. Use one comma before to indicate the beginning of the pause and one at the end to indicate the end of the pause.

Here are some clues to help you decide whether the sentence element is essential:

* If you leave out the clause, phrase, or word, does the sentence still make sense?

* Does the clause, phrase, or word interrupt the flow of words in the original sentence?

* If you move the element to a different position in the sentence, does the sentence still make sense?

If you answer “yes” to one or more of these questions, then the element in question is nonessential and should be set off with commas.

http://owl.english.purdue.edu/handouts/grammar/g_comma.html

I run on sometimes, so I ought to know.