I understand what you mean, I'm in a similar situation. It's tough not having a place of your own and the ability to pay for rent. You could wait until you have some financial independence, but you have to ask yourself if you can wait that long. If so, then it isn't a bad idea to save up and get your own place. However, if you feel a burning need to come out (like a huge amount of depression), then you might want to consider coming out sooner than latter. Doesn't have to be today, but remember there will always be roadblocks and things to prevent you from moving forward.
Keep in mind, you don't have to wait for your mother's approval before you start hrt, see a gender specialist or go to a group meeting. Coming out doesn't need to be the beginning of your transition. It hasn't been for me. You can start secretly in the beginning and make some major progress. Yet, once you start hormones and trying to pass, you are on a timeline.
So, don't sweat it that today didn't work. You have many other options available to you and will be able to do this successfully when you feel ready.