Can you develop a stutter?

Can you develop a stutter? i've always had pretty terrible anxiety when talking to people i don't know. however my speech, while infrequent, was usually intact. lately, though, i've noticed myself repeating the start of a word and falling over in my speech and having to start over. however, this doesnt seem to be a general pattern with my speech, it only happens when i am talking to an unfamiliar person. what is happening here? this is not normal for me. is this a stutter, or is this a different issue? why is this happening?