A good career is that one that you really love, the one that enthusiasm you and makes you want more. If SEO does that, then it would be.
Additionally of course, your want to make a living.
1) SEO, for my taste, lacks exactitude (like most marketing fields, I have to say). It is a field full of misconceptions and wrong information. You'll find loads of information on the internet but most of it is just rubbish. Most of those who called themselves SEO experts don't have a clue what SEO is (and again, this happens a lot in the broader world of marketing)
But it is true that's something that you can study by yourself because there are no university studies for it.
2) Studying at university will help you in the future because you will have a formal degree and because you will learn to discipline yourself (at school you had your teachers rating you all the time, this doesn't happen at University where schedules are more relaxed and you're not forced to stay in the class. I suggest that you do, if you decide to go). There's no degree for SEO. SEO is a mix of marketing and web development. If I had to choose, I'd go for a computer science degree
3) The only degree that may be of any help, I think, would be Google Adwords and Marketing certificates. I don't think there's anything else that can be recognized globally.