To get your license corrected, you'd need a court order for a name change and then you'd need to follow whatever process your state has in place to correct your gender marker. It varies from state to state. In some, it's another court order. In some, a doctor's note will suffice. In mine, I had to have my doctor send a letter to the DMV headquarters and then the DMV mailed me a letter to take to the local office to have it updated. Since you're under 18, you would likely need parental approval for both of these things. I believe the DMV cross-references Social Security when they input your information, so you can't just tell the government to put a preferred name or to change your gender on your license. You'd have to get everything legally taken care of, updated with SSA, and then update at the DMV.
As far as work, I applied for things with mixed documents and just let them know what was going on. I would fill out the application as my new name and gender, and then if there was a background or reference check I'd make my previous name and court order for my name change available so that there were no issues.