PMP Project Management Experience Question from a new college graduate

Hello,

I was wondering exactly counts as project management experience. From everything that I read before, I was under the impression that it was professional (i.e. on the job) project management experience, but then I read this thread over at StackExchange that muddied things up for me. To me, it sounds like "project management experience" can come from non-work situations too, such as extracurricular activities.

My situation:
I completed the Coursera Project Management Specialization, which means I meet the educational requirements to write both the CAPM and PMP, and I was initially just planning on writing the CAPM.

I just finished my undergrad in Electrical Engineering last December, but I also have about two years worth of internships and co-ops. I also have about two years of Web Development experience on a part time basis, and a lot of extracurricular (student organization) experiences too.

My question is can I really count my internships, part time work experience, and extracurricular and class projects to count towards the PMI's 4500 hours requirement?

Thanks in advance!