I say get a job. You are so melodramatic, like if you pick a EE job, you are going to end up doing it for 40 years. How about just doing it for a year or two until you figure out something better to do.
I am a EE, and I got a job at a processor design house, and I like it so far. Yeah, simulations are tedious, and it's hard work, but come on. What did you expect EE's did? I only have a BS. I specifically wanted to see if I liked the work before I went on to get further degree. I am going to give myself a couple more years to see if I get bored. If I do, I will get a masters to change my course. If I am still happy with my career, I will get a masters to speed me along the course I am already on.
If anything, you'll learn how things work, how the corporate world runs, learn how to build and productize things, and make some money to comfortably afford graduate school.
Oh, and if you have computer/electrical engineer on your resume, your resume will stand out. It basically says that not only are you smart, but you can learn very complicated things pretty quickly.