Got a blog, promote it. Check your Google Analytics and see if you can move your organic search success up the ranks. Run a Facebook ad, learn the system. You can pay "per-click" and limit the budget to $5. That's pretty reasonable. And then keep writing good content and see if you can up your readership, your stickiness (how many people subscribe or return to your blog - "returning vs new" on your Google Analytics).
There is nothing 9-to-5 about social media. You might work office hours that look like that, but the REAL social happens after hours and on the weekend. Sorry to break…
So, take heart, you can go from what ever degree you just earned and get into communications and it will help every presentation, every email, every contract you have to write from here on out. AND if you are so inclined, Social Media is pretty much based on writing. If you can WRITE, and write well, you have a head start over everyone else, regardless of your degree or desired specialty.
Are you thinking about starting a blog? Are you working, leading, exploring social media as a career? Okay. So if I Google your name, or your Twitter ID I'm going to find... what exactly?