Gee my oldest daughter is twinsplusone too!!! :-)

Anyway... I have the same type of pool and this happens to me every single year to one degree or another.

It's rust. :-) Your water must have a high iron content and when you add the chlorine it causes the iron in the water to rust. My kids will swim in this if desperate enough. ;-)
Just wear old stuff as the rust stains light fabrics.

You need to add something WHILE filling it and before you add all that chlorine to it. Don't ask me what to add... came to the forum looking for that answer before I set my pool up this year!!! ;-)

So what to do now??? Rinse your filter OFTEN( a few times a day!!) and wait. :-)
It will filter out, but it's takes a few DAYS!!! Depending on the size of your pool. My smaller pool took about a week, my larger pool, about 2 weeks. I set up my small filter with the larger one so it filters faster.

Hopefully someone will have a better solution, but just know if all else fails, time and filtering will take care of it and it's not really 'dirty' water- just rusty. ;-)

You will want to buy another filter too as filtering all that rust out is going to do in the one you have now.

Carol in IL