Not easy for a teen to do but try looking at this from your mom's point of view...
It won't sound reasonable to you but the behaviour of you and your brother is how other people judge your mom and how your mom feels she is judged - you might have heard stories about a corrupt cop whose behaviour taints an entire police force so nobody trusts any police officer because of one bad one?
Friends and neighbours will judge the quality of a whole family on the behaviour of the worst behaved member of that family - having a food fight with anyone in a public place made your mom feel humiliated; something she is justifiably angry about - even worse she was betrayed by two members of her family at the same time...
AND it cost her a chunk of money to a complete stranger which piles humiliation on humiliation...
Your mom wants to be proud of you and you disappointed her. Cribs and pampers is something of an over-reaction but she does have a point and she is telling you how she feels about the whole situation - I guess you got the mom you deserve and the fact she cares about these things means you already have a better mom than most!
As long as you believe she is a bad mom for caring about these things her comments about your bad behaviour have a basis in fact...
I strongly suggest you begin to put things right by, not only saying sorry in the most humble way you can, but finding some way of earning the 45 dollars to pay her back in order to begin to prove, not only how genuinely sorry you are for humiliating her in public, but you really are mature enough for driving privileges and so forth!
As long as you blame your brother for starting the fight proving your maturity is going to be a uphill struggle - at 15 you are two years the elder and would normally be around five years more mature than he is so the greater responsibility is your own!
Even if you can't believe what I have told you, it is time you learned that skilled diplomacy is the way to get what you want - life is a two-way street and in the normal way of things you have to give a little in order to get a little. A mature person knows these things instinctively...