The short answer is: yes. Especially LinkedIn.
The longer answer is somewhat unrelated. If you never really interviewed or applied after college, it's going to be crappy if you take all the resume/application/interview classes seriously.
On the resume part, fill up your resume/LinkedIn profile. If you've done 'various QA and product roles' and 'project management to product management', make sure to write them all down as separate experiences within the same company. With every experience, add a start and end date, doesn't matter if they overlap or if you don't know exactly, it doesn't matter. Also, add the technologies, skills and other relevant info per experience. This way, you show growth and broad knowledge.
On the application part, I have noticed that a warm entry is the best. E-mail a recruiter with a question about a role anything is fine. Their response will tell you a lot about the company. Sometimes they ask you to just send your resume and set up a call. These calls are a much better way to introduce yourself than a cover letter. Sometimes a cover letter is necessary though, if it is, at least write something honest. You can also just pick up the phone and call a recruiter, that also works sometimes.
On the interview part, my most important advice is that it's a two way street. Not just the interaction, that's what they teach you at school. It's a two way street in the fact that the company should also be somewhat trying to convince you to work there. Especially because you have skills that are sought after. So don't feel like you have to impress the company too much, be yourself, be honest (of you can't answer a question, say that, don't make something up) and think of it as a conversation, not an interview. That can really help with the nerves too.
Finally, don't get discouraged. There are many shitty HR departments, shitty manager, shitty companies and of course, shitty interviews. If that's the case, just realize it's them not you. You've dodged a bullet by seeing that and you can continue to the next interview. I once rejected an offer because the interview process gave me such a bad vibe, that I couldn't see myself working there. And beyond shitty interviews, sometimes you're just not a good fit for a roll or company and that's fine too.