I don't know if you had the same experience but I think for me the key to succeeding in this transition was to try and learn not only to 'code', but also about the engineering, quality, deployment processes surrounding code that most juniors (that I have seen) typically know little-to-nothing about.
That way, even if you have a lot to learn on-the-job, you probably won't be a burden on the rest of the team and they won't have to spend too much time holding your hand (except at code review time, but I guess that's the case with every newcomer to a project).
I also worked for myself for some time and had some experience (minor really) to help me get my foot through the door. Then when you get a job, you have an opportunity to show what you can do and after that you're just like everybody else.