The first thing I'd have to say is if you are having these thoughts, to contact a psychiatrist or therapist, they will be able to help you deal with the anxiety you feel from having a prosthetic leg. A prosthetic leg shouldn't bother you though, it's nothing to be ashamed of, depending on how large the prosthetic is (if it's below the knee then it's almost barely noticeable in some cases, wear long pants and you'll be fine). But of course, I can't imagine the feelings that you're going through now happening to have gone through all of that, but I will tell you there is nothing wrong with a prosthetic, it tells that you are a survivor, that you've been through something not many people have and for that it can make you a better person. There are people everywhere, including me, who worry about needless details, but we are unable to get the a truly wise experience from something like that, your prosthetic says you're strong, you're powerful, you're wise. I don't see why it would be shameful, but again I can't imagine what you are thinking.
For your job, if your dad doesn't believe you ask him for help finding a job. If he accepts there are two possible ways that can turn out.
1. You can't find a job and then he realizes how hard it is
2. You can find a job and hey! You've got a job!
It's important to communicate with your family members how there actions affect you, tell your father that the reason you haven't been public about is anxiety from your prosthetic. Do it in a nice calm manner though, definitely not in an argument, just sit down with him and calmly and politely tell him the reason he hasn't been out, and maybe that you want to see a therapist (if you do, I think it'll be a good idea maybe). Unless you already have a terrible relationship with your father, he should understand in some way.
Also a job is important, if you get a job when you're young it makes it much easier to get job when you're older. I know it sucks cause you want to do the stuff you want to do, but another big plus with jobs is you get money, you get quite a bit of money relative to an allowance. I'm not sure where you live so the wages are dependent but if you make say $10 an hour, and you work 5 hours a day for three days, you make $150 a week, which (for me anyway) is a good sum of money!