It's entirely possible that the stress you're feeling is making your lips worse. I could tell you it's not that bad, others have it much worse, etc... but that's logical and you know that. We're talking about an emotional response which you are entitled to.
I would encourage you to get and do something athletic on a daily basis. It helps with stress & Depression (and by lowering your stress you may get added benefits of lip improvement). Most people in the gym are completely absorbed in their own insecurities to notice anyone else.
Consider doing some volunteer work, just because... doesn't have to be about seeing people who are worse off than you. I do a lot of work with animals because I'm an animal person. They sure as hell don't care what I look like, and I feel good about helping them. It's just good to get out of the house and feel productive.
Finally, and I realize people here may not support this statement, it's ok to seek professional help and take medication for Depression if you choose. You're a young guy and you deserve to be happy. Exercise has been proven to be as effective as medication in mild to moderate depression, but major biochemical depressions may need more than that. It's an option worth exploring before you do something permanent.