Confidence is key when asking for a raise, and the strength in your argument and poise in presentation should come from your accomplishments and conviction that it's the right move. Listing your personal financial hardships should be left out of the equation when approaching your boss; if you really do need more money and are ready to take on more responsibility, find out what you can do to make yourself more valuable.
While I think the point is pretty clear, Michael Zwell author of Six-Figure Salary Negotiation said it best: "When we were young, our parents told us that if we wanted money, we had to earn it. So, we mowed the lawn, did house chores or watched younger siblings to earn a buck. Similarly, if you need more money per paycheck, ask your boss how you can contribute to earn a little extra."