I am going to disagree a little bit here. This could be the first time you are noticing symptoms. My advice is see your provider to have them investigate the sores and do a culture test if the sores have been there less than 48 hours. This way you will know for sure if it herpes or not. Also have your partner look into a type specific IgG blood test to know their own status. Chances are you both unless you have asked for it have ever been tested for HSV.
the short answer is yes, it is possible