Will I get in trouble for this at work or is it really nothing?

Hi. I work in a building as a student temp worker doing an internship. There's a girl there that came to me a couple of times in my room. She likes me and wanted to get to know me. We eventually went out from those two meetings. Not long after, I found out there was a camera in the room recording us and I didn't know it. My temp company boss says that was distracting my work and I can't talk to her again. My supervisor even asked me where I went with her outside of work. The girl employee was confronted by her supervisors too with a courtesy meeting about it. She said there's nothing to worry about because us talking on those two occasions really didn't affect our jobs. But my internship supervisor automatically judged me saying it distracted my work but It didn't. I like this girl and we're friends now. She wants to date me. My temp internship ends in about a month from now. My supervisor said I can't talk to her anymore and to tell her to leave my room if she comes to my room again. I want to get a full-time job there after my internship ends or in one of their other companies in their big organization. People at work talk to each other all the time. But my supervisor told me temps aren't supposed to talk to the regular workers if it doesn't concern my work. Can my supervisor tell me who I can talk to, date or hangout with after work hours or only at work? Will this affect me in the future? Or is it something small and will go away after next month? I'm worried. Thanks.