Dr. Colin Gibson
As long as you are able to close your lips around the braces without any discomfort and have not had an extractions (tooth removal) in conjunction with your braces, you should be fine to drink through a straw.
The brackets and wires on the front of someones teeth can cause sores or feel like their lips are being stretched. They make orthodontic wax to put on the braces to prevent this.
Also sometimes people need to have teeth removed in order to make room for all the rest of the teeth. The teeth are usually extracted before the braces are put on, but dry socket is always a condition to consider when teeth are removed.
Hope this helps.
My best to you!
William F. Scott IV, DMD