The following advice is only worth what you paid for it, so keep that in mind.
If I were you, I would do everything I could to get a job as an electrical engineer doing actual electrical engineering *design* work. Try and get at least a good two to three years of design experience. If you have to work as an intern to get the job, then do it.
Meanwhile, go out and buy a patent bar review course. You can get a good course for about $550 bucks used which includes hours of audio, some lectures on DVD, some books, and an explanation of how to pass the exam. Watch and listen to the lectures, do some practice exams, and familiarize yourself with what is involved. Then, when you have some serious time and motivation to really dedicate yourself to passing the examination, start from the beginning and do some intensive study with a focus on prior exams. Go take the test, and become a patent agent. Whether you go into intellectual property work or not, you will always have the registration as a patent agent in your back pocket. A month of studying and a day taking an exam isn't much to ask for to have an additional marketable skill.
After you get some *design* experience as an electrical engineer, then you can either continue that path or go after the (sometimes) higher pay involved with management, marketing, or sales on the technical side of electronics.
With some experience and money in your pocket, you can take a good look at going for that MSEE degree (knowing, of course, that you are also a registered patent agent if you ever need it). Or, if you still have a passion and interest in law, then go into law school. Right now the way the market is, the opportunity cost of law school doesn't look like it is a great payoff unless you go into it because you believe you will love the work and business of law.
You are 21. Done with your BSEE by 22. Few years work experience by 25 as a design engineer. Opportunities from that point forward will look a lot different. Your path will be more clear. Maybe you end up changing your mind and want to go into management, marketing, more advanced electrical engineering, or maybe even intellectual property law.
One thing is for damn sure... be sure to continuously do something to improve your skills every year. I personally spent many years as an electrical engineer and I became very very skilled at my job, but at that particular job. What I didn't do is spend time outside of work mastering other marketable engineering skills. Learn from the mistakes of others... it is cheaper that way.
If the politicians that we get in the future are anything like the politicians that we have had over the last decade or so, then you are going to need every little advantage you can get.