If I get a higher paying job, do I automatically have to pay more for my daughter or does my ex have to take me back to court to get more? Also, if I have another child w my new wife, can I get my child support lowered?

Child support is determined in the US by specific state laws, so how your pay depends in the US on where the support order is at.

Next what does your child support order state, are you required to report a change in earnings?
In most states the change in amount is done at request but does not require a hearing, you are asked and perhaps the other parent asked to provide proof of earnings, then a new amount is set.

But yes of course if you earn more you are suppose to pay more in most cases, in most cases support is a percent of earnings.

The issue of a child with your current partner does not matter in most areas,