First off, many congrats. Most junior college students I have met who finished were working adults/older teens and they earned their 60 units the hard way, with kids, jobs, sleepless nights, etc.
I say go, and if not for your parents for yourself and your school and your classmates. But if this public type of ceremony makes you uncomfortable, then don't go and don't attempt to explain yourself. For some people, this type of thing is a phobia.
Before I finished college, I put in my dues at JC, both as a youngster living at home with no other worries, but then later as an adult with a lot of other responsibilities. It was seriously harder to finish some junior college courses for AA than some upper level courses toward a bachelor's. You should be proud of your achievement, and whether you had to struggle or not, there are so many people who typically go to a junior college who have to shoulder a much larger load than just going off to university and having parents pay for it (like I did unsuccessfully the first time
).
When I finished junior college, I had the same deadline to meet that your have to be in the graduation ceremony which I missed by a week since nobody told me. By the time the next year came around in June or late-May, I had finished my bachelor's and it just fell into a schedule that I could go to the BA ceremony on a Friday and AA event on that Saturday. Stupidly, when I inquired, I was a day late so I couldn't walk in the ceremony. But I went and sat in the audience anyway and got to see former classmates get their degree. It was great to see the ceremony and I was happy I went.
I say at the very least, show up in the audience. It's not every day you finish high school, college, junior college, or a professional/trade school.
