What I learned was to leave off everything from undergrad except your degree in the education section. You can also include you major(s) and minor(s), and if you graduated with any honors in that section.
That said, I learned this as a graduate student applying for faculty jobs. I would say that you can probably leave your undergrad achievements on you CV during the first few years of your graduate program, but as you advance further in your career, I would eventually remove the undergraduate items.
Regarding your paper:
If you're interested in a career in academia, my advice is this: if the quality of your paper is exceptional, and/or there's room to further develop it to merit submission to a professional journal, I would try doing that instead, otherwise set it aside for the time being and focus your energy elsewhere. In academia, publications in student journals typically don't weigh much, unless it's an especially reputable one. I can't speak for expectations in other industries - a publication in an undergrad journal might weigh more for non-academic jobs.
Best of luck with your PhD program!