Don’t hesitate to start a sentence with Yet. It’s a coordinating conjunction, and great writers have been starting sentences with conjunctions for hundreds of years. You can remember the coordinating conjunctions by referring to the acronym BOYFANS: but, or, yet, for, and, nor, so. You can begin a sentence with any of these. And you should.
You’ll find a complete discussion of coordinating conjunctions in the Parts of Speech section of Grammar.com. Click here for the beginning of that discussion.