Chances of norovirus?

So I’m currently a PCA who is starting ABSN prerequisites and honestly I’m terrified I’m gonna be a terrible nurse. I have pretty bad emetophobia and I’m really struggling tonight so I’m just gonna post here and ask a question that probably sounds insane so I’m sorry in advance lol. I work in a psych emergency room and earlier tonight I took vitals on a patient (I wore gloves but no mask) and about an hour later he went to the bathroom and vomited a few times and then went back to his room. Apparently he said that this has been happening recently after he eats and that it’s been worse the past few days. I was maybe about 20 ft from the bathroom (door closed) while he was vomiting and I’m terrified I’m gonna catch something like norovirus from being close to him while taking his vitals or from being close to the bathroom. What are the chances he even has norovirus if he says this is a regular occurrence? Am I gonna catch something? I’m sorry if I sound really dumb but I’m really anxious and I would love to hear some insight from nurses.