How can I best improve my skills/experience for graphic design and related creative jobs?

You might check to see if there's an Adobe User Group (Adobe User Group directory) near you. If not, see what Meetups are near you. You can improve your skills while networking which could lead to some work. If you'd like to practice some skills, see if there are any volunteer opportunities for non-profits in your area.

If you'd like to check out various digital media areas, look through last year's Adobe MAX sessions (Adobe MAX 2016 Sessions). If you're still a student and would like to come to this year's Adobe MAX, you could get an educational discount (Adobe MAX—The Creativity Conference.) or watch online once those become available.

I don't think doing a general course in digital media and animation is such a bad thing. Your main problem is going to be for you to decide in which direction you wish to develop your skills.

you may wish to develop them in a traditional media direction such as tv and video, or concentrate on animation or move in the direction of new media such as delivered by the web. All these are open to 'exploration' before you make a final decission, but everything will depend on what you decide, find interesting, and if you think advancing your skill set will achive whatever it is you wish for your own future career.

If you need ideas/help with a specific Adobe program, asking in the forum for that program is where you need to start

Here is the list of all Adobe forums... https://forums.adobe.com/welcome

You should also Google to find tutorials for the program(s) you use

Graphic Design covers such a wide swath... what's your area of specialty or greatest interest?

Which software products are you using proficiently?