Oh ya, it's possible. I have done it. I normally will wake up while doing something if it is active enough. I woke up running outside my house in my pj's, I kid you not. That was scary. This stopped for me in my mid 30's. Not sure why. The only thing I narrow it down to is being sleep deprived and stressed. It happened particularly when I started college and then when I was single living alone and then the first few months after I got married and my husband and I started living together (maybe that was stressful. ha ha, and it took a while to get used to every night sleeping with someone). Anyway, agree to talk to your doctor. It's not really bad to do it except you can get hurt in that state if you leave your bed. (IE: running down your street).
Suggest you mention this to your doctor next chance you have. There is something called a REM sleep disorder that could cause something like this. Not saying you have it, and if you have no more incidents going forward you'll probably just outgrow it. But if it lasts and you are concerned, talk to your doc because it is treatable.