If your family was supportive of your artwork growing up, you have a strong emotional advantage going forward. You have less baggage and less guilt. You don't have that nagging feeling that you're wasting someone else's time or money. You'll even be more bold in your expression since creativity was always supported in your home.
However, if you're in an environment that isn't supportive of what you're doing, you might want to find a new one. It doesn't have to be family; it could be roommates or even a group of friends who are discouraging you. If that's the case, leave. By all means, do so cordially, pay all the necessary close out bills and find a replacement for yourself if necessary, but leave. You don't need that kind of negativity in your life when it's already hard enough to concentrate on your goals.
A healthy environment to work in isn't going to fix everything though. You still might encounter people in school or in the workplace who drag you down. Constructive criticism is one thing, but if people are telling you can't do what you love because you haven't had schooling for it, or if someone says your medium is outdated and on the decline, you need to find a way to become invulnerable to this. I can't tell you how. It takes work.
But change everything that it is within your power to change if it's slowing you down. Make no apologies for what you create.