Have I been networking wrong?

I'm a sophomore at a target public school with a good GPA but no experience. Since September, I've been cold emailing as many alumni as I can, have had phone calls with to about 30 people, from analysts to MDs for both sophomore and junior year internships. However, part of me feels like I'm being ineffective with my approach, as I never considered if they were directly involved with recruiting. My plan was to follow up with these people every three months, and eventually ask for a resume push. Have I been doing this wrong? Or can anyone help push my resume?