Do you think a software engineer degree is worth it given my current experience?
1) You get a thorough and broad knowledge about the subject. Many self-taught programmers focus on just the stuff they need at the moment, and lack a lot of the breadth that comes from full time studying a subject 3 - 5 years.
2) You'll get to know many people in your field, both students and professors, and depending on your university, you might even get contacts to the industry. This is neat because first of all it's fun to meet like minded people, and second of all you'll get to be part of a network that makes finding jobs much easier.
3) It's much easier to find a job when you have completed a degree. A completed degree gives you instant credibility. You can of course get a job without a degree, but every time you apply you're going to be playing in hard mode, especially when all the other candidates have a degree.
Long answer: Depends on your situation and your goals. I was like you in that I had 2 years of programming when I decided to go to university (CS degree). At that time, no one would hire a kid who claimed he knew how to program. So my entire goal was to get a piece of paper that would validate I knew something.
Somewhere in my Junior year, I was grateful I was in school. I think it was Algorithms that did it for me. It was so exciting and enlightening.
That said, I have know successful programmers who did not get a college degree, and worked their way up, one painful step at a time. In all cases I truly believe they would have been more successful had they gone to school. But, depending on your life circumstance that is not always possible.
Do you have a good quality school in mind? Can you afford to go to school?
EDIT: change "softeware engineering" to "STEM"
If you are motivated you can learn most of what they teach at university from text books and by using online materials from the best universities. The hardest thing about being self-taught is that it is hard to find competent help when you get stuck.
Ideally you want a job where your co-workers can help you out when you get stuck. You might notice that many of them do have degrees.
Where do you live and what's the cost of a degree there?
Why software engineering and not computer science?
I really think it's worth it given that you're only 19 - you'll learn a lot, it will open many doors (especially if you go to a good university), and you'll get a chance to grow up a bit in your early 20s in an environment that you can't experience otherwise.
Some universities have something like a studium generale, which I don't think hurts to evade the narrow perspective of computer science. Otherwise it doesn't hurt to look into other fields.
On the other hand you can also study another engineering discipline and be a good programmer, but I believe that most content in computer science is worth it. At least at my university that was the case.
If you have an average IQ and/or if you find programming more of a "job", then you need a degree. In this capacity, even though you should be programming, you'd rather be gaming or doing something else.
I'd echo any others who say that a degree is worth it. S/W engineering, maybe, maybe not.
A degree is a signal you can stick at something for four or five years. This is a valuable skill. You may have that skill without a four-year degree, of course, but the signal isn't there. My first job took me a few years to feel comfortable because I'm a slow learner and the technology was difficult to learn at the same time as the rest of the job.
Should you do software engineering? Programming is a white-collar trade skill. You can do a lot with programming, and a degree doesn't magically confer the trade skills.
I usually recommend people who are degree interested to consider mathematics for a bachelor's degree and then a masters in Computer Science if they're interested in graduate-level education. This isn't the way I went, though, so I can't comment on whether it's really that advisable. But I would think a rigorous math education would prepare you for thinking about fun problems you can solve with programming and an MS would provide some research to go along with it.
When your 4 years (+/- 1) of listening to smart people is over, you've probably learned something. This probably includes things you didn't know you wanted to know. I didn't know linguistics existed until it was the only elective that fit into my timetable. I ended up enjoying it so much I nearly changed majors.
Theres value in a getting a degree to get certain jobs, but msot of it is in the sheer volume and breadth of things you learn. It's also a great excuse to socialize with people who are interested in the same things.
Your existing programming experience will give you a head start in a few courses.
Most importantly, it will be easier for you to get an internship while studying and you will get exposed to real world software engineering in a hopefully successful software company.
The degree will also make it easy to relocate across the globe. Some countries require university education or many years of experience to even let you work there as a software engineer.