If I have a class B misdemeanor arrest on my record, will I still be able to apply to get my medical license in Texas?

You need to be very careful with that case. Shoplifting is basically a theft. Class B means that the value of the goods alleged stolen was over $50. In Texas, theft is considered a "crime of moral turpitude." Basically, it's a crime category that is used to say a person is a "bad person." In my opinion, there are not many things more undesireable to have on your record. The "community service...class...and charges dropped," you mentioned, sounds like a probation. But, beware, there is more than one kind of probation. There is one potential resolution of your case that could allow you to have it expunged, down the road. There is another potential resolution of your case that could allow you to have it sealed, down the road. And there is yet another potential resolution of your case that will foreclose both options.  With or without a conviction you'd be able to apply for a medical license. That's not really the question. The question is whether a potential conviction could prevent you from receiving your license from the medical board. I don't know that even a theft conviction would be an absolute bar to your getting licensed to practice medicine. Usually, (at least with lawyers) there is a review process, at which you can make a case for why you deserve to be licensed, even with the conviction. Of course, the better option is to not have to deal with that at all. So, you need to be sure that whatever path to resolution you choose, gives you the ability to have it expunged, down the road.