So you are wondering about another rule that English teachers tell you that is really a "myth." It's that you can't begin a sentence with 'and,' 'but,' 'or,' 'yet,' or 'so.' Well, you can.
Your teacher might correct you when you begin a sentence with "and." However, as long as your sentence is an independent clause, it's fine, and many of the best writers start sentences with those words mentioned above, including the word "and."
In fact, it would be very embarrassing if there were a rule that stated one couldn't begin a sentence with 'and.' Just look at the beginning of the King James Bible:
In the beginning God created the heaven and the earth.
And the earth was without form, and void; and darkness was upon the face of the deep.
And the Spirit of God moved upon the face of the waters.
And God said, Let there be light: and there was light.
The reason it would be embarrassing is because King James gathered the most eminent writers in all of England to render a new translation of the Bible, and if they had used improper grammar, the King would have been pretty upset (not to mention a lot of other people).