The short answer is yes;
there is nothing grammatically wrong with starting a sentence with a conjunction like but, and,
But this answer comes with a warning.
The idea that you shouldn't begin a sentence with a conjunction is one of those "rules" that really isn't — along with some others you've probably heard, like "never split an infinitive" and "don't end a sentence with a preposition." Your writing won't be automatically bad if you break these "rules," and the greatest writers of English have been breaking them for ages. For example,
- From Herman Melville's Moby-Dick: "Despairing of him, therefore, I determined to go to bed and to sleep; and no doubt, before a great while, he would follow me. But previous to turning in, I took my heavy bearskin jacket, and threw it over him, as it promised to be a very cold night . . ."
- From R.L. Stevenson's Dr. Jekyll and Mr. Hyde: "In this character, it was frequently his fortune to be the last reputable acquaintance and the last good influence in the lives of down-going men. And to such as these, so long as they came about his chambers, he never marked a shade of change in his demeanour."
- From Nathaniel Hawthorne's The Scarlet Letter: "Not seldom she [Pearl] would laugh anew, and louder than before, like a thing incapable and unintelligent of human sorrow. Or — but this more rarely happened — she would be convulsed with rage of grief and sob out her love for her mother in broken words, and seem intent on proving that she had a heart by breaking it."
But before you go off with sentence-initial conjunctions, consider your audience. If you're writing a paper for your English class, your main audience is your teacher or professor. If he or she lives and dies by the prescriptions and proscriptions of a favorite writing guide, you'd better stick to the injunctions in that book if you want a good grade.
It's a fact in the publishing world, and especially in nonfiction, that hired authors are often expected to write according to a house style guide created by someone else. These style guides can dictate anything from whether to hyphenate underachiever to whether to treat data as singular or plural to, yes, whether or not you can begin a sentence with a conjunction. Regardless of your own style leanings, you're expected to follow the dictates of that style guide. And so it can be in school.
However, most teachers understand that great writing doesn't come from strict adherence to grammatical rules any more than great cooking comes from strictly following a recipe. In short, unless you know that your teacher truly believes that a sentence should never begin with a conjunction, it should be okay to do so.