You absolutely must give measurable achievements. Team size, number of documents authored, anything! Prove that you worked somewhere and didn't just take a paycheck for breathing.
> my resume (it's three pages)
Cut that down to one page.
> But most jobs have either not replied to my application or I've been rejected a week or so after submitting my resume.
You are still in the phase of your career where you are applying for jobs so rejection will be common. Apply for at least 3 jobs/day if you can find openings. Expect to put in hundreds of applications.