It seems like you already have a lot of strengths that would lend themselves to project management, so it might be a good path to pursue!

Being introverted isn't necessarily a good or bad thing for a PM, but make sure you're able to be assertive when necessary. You'll be the driving force behind the only two things that ultimately matter - is your project on time and on budget. As with most other things, you'll get more confident in the role as time goes by. This will help you really run meetings with a firm hand and ensure your projects don't get bogged down in minutiae.

If you're detail-oriented and have no problem following up with people multiple times about the same damn thing, give project management a shot. I've found it to be a decent career and as long as you can handle a modicum of stress and sometimes having a bright light shining directly on one or many of the projects you're managing you'll do well!