Here's why you need to show that you can take care of yourself, regardless of who you are living with. Just suppose that at some point you and your boyfriend break up. Yes, I know, at 16 you're quite sure this will never happen, but take it from someone who's been there; it does.
So you've been living with your boyfriend and now you're on your own. His income has been part of what was paying the rent and utilities and food bills. You have to be able to fill the gap. You have to be making enough to cover everything he's been paying for.
Many employers will not hire you for anything over a minimum wage job if you are not either in school or a high school graduate. So dropping out of school so that you can get a better paying job or work more hours on the one you've got isn't necessarily the answer.
By the way, you haven't explained what kind of abuse you are being subjected to. If you're being beaten you have a far better chance of being emancipated, (assuming that Texas permits it, which we haven't established yet) than if the abuse is verbal. Or, like one kid I talked to a few months ago, if the "abuse" means that your parents are insisting that you follow a curfew that you think is unreasonable, requiring that you get decent grades, and insisting that you occasionally sit down with the family at the dinner table and talk politely to your Aunt Susan. I'm not saying this to put you down; just pointing out the reality that what you consider abuse might not be, legally.
If you really are talking about physical abuse, have you called the Child Protective Services? They may have alternate methods of helping you that do not involve putting you out on your own when you are clearly not ready for that.
Emancipation is not supposed to be easy to get. It is for those rare cases where the minor is clearly better able to take care of him/herself than those who are responsible for him/her. Again, I don't mean this to put you down but I remember what it was like to be 16. I know you feel like you're able to take care of yourself - all 16 year olds do. But it really isn't as easy as all that.