You will need to ask your unit at your school. Our school did not permit individual swear-ins. They were done as a group, even though there were parents who were active duty Navy officers, in uniform, present.
The NROTC swearing in is very different than commissioning. At commissioning, it is common for graduates to have family/friends swear them in, if they are eligible. However, you'll find that that most units will simply have their CO conduct one oath for the whole incoming class at swearing in. It has nowhere near the significance of commissioning, so I wouldn't worry about it.