Hello Aimee, While I didn't major in astronomy or computer science, I did take classes in both for my B.S. engineering degree.
On the computer science side, the Institute of Electrical and Electronics Engineers (IEEE) is a great student/professional organization to be involved in, and most engineering programs will have a local student-run chapter. lEEE home
On the astronomy side, it looks like there are a number of ways you could get involved: NATIONAL ORGANIZATIONS American Association of Variable Star Observers (AAVSO) Association of Universities for Research in Astronomy (AURA) Astronomical Society of the Pacific (ASP) American Astronomical Society (AAS) Universities Space Research Association. Midwest Astrochemistry Consortium.
If you want to work at NASA in the field of astronomy, my best advice is to seek out opportunities for teamwork and leadership, via research projects at your school or in student organizations. NASA looks to hire technically competent and strong leaders, with great interpersonal and soft-skills like verbal communication. It's an amazing place to work, and the people who you work with are some of the best in the world and the most passionate about what they do. So aim high, "shoot for the stars" may be cliche but it sounds like it applies to you. Good luck!