Just do it.
Know that you're taking a risk financially, because there's no guarantee for work (you have to be active in finding it) and there are a lot of people working in and studying for the field, with the same or stronger determination as you. So you need to be active in networking and giving yourself out as someone that people trust and will want to work with or hire instead of person B. But don't get into some stupid "I'm competitive" mode, you need allies and your attitude has to be sound (among the people that you work with). It can take a lot of time (like closer to 10 years or more) to form a professional network where you can find work as a freelancer/entrepreneur. But you can also get lucky or get a position in a company (which although isn't necessarily secure either, because smaller entertainment firms or sound houses tend to be quite volatile, bigger as well, because that's the nature of the entertainment industry). One key to boost your employment prospects is to be versed in another art form or skill that's applied in the medium that you work in, in addition to sound. You definitely shouldn't pursue this because of money, but rather because it's like "the only thing" that you want to do and you want to do it professionally, rather than semi-professionally/as a hobby and getting your income from other sources. You need determination and motivation or you can burn out, you need to know that the work can be quite hectic and stressful at times (deadlines) and you may need to do creative work even when you're not inspired or personally don't care about the product that you're working for.
I would not overstress the decision as a "very important life decision". I think you should approach it primarily as a fun hobby that you like to do, rather than "a job". If you get paid for it, then that's even better, but you shouldn't base your decision on it. Be ready and open to other stuff as well than just sound/music. If you plan on getting a degree, then you should think very carefully, I wouldn't recommend going into debt because of this.
Technically, your (main) tool is a DAW and a combination of microphones and recorders. What operating system you run is irrelevant, but macs are fairly popular, because OS X is technically simple to operate and poses far less problems with maintenance, drivers and stuff compared to Windows. And Apple's computers are pretty. Linux is very rare/almost non-existent in audio post work, because it doesn't have the necessary software (Pro Tools, Soundforge etc.), unless you run it through Wine. You can easily google for "linux audio software" and see what's available. I believe Ardour is the only formidable Linux DAW. Again, if you're only working by yourself, then you can choose freely what you use, but usually not, if you have to sync files with other people.
Pd is useful for learning about interactive sound sequencing and high-level audio and midi processing. It's not very relevant for "sound design", unless you have a very specific idea for a patch that you use it for + it's definitely not a fast tool to work with.
Oh, and I don't know how applicable advanced math and physics is in "sound design". This is an art field, or alternatively a trade/craft. I mean, if you want to program software, design hardware or design e.g. acoustic spaces or simulations, then definitely, and I personally stress the study of natural sciences as general education, even if you're not applying the knowledge, but for doing "sound design" i.e. soundtracks for media in the general sense, it's not that relevant, nor common. This work is about feeling, rather than formulas.