Swimming is great for many reasons - but it is not an effective way to lose weight:
http://www.thefactsaboutfitness.com/research/swimming.htm To lose weight, you want to raise your body temperature and actually sweat. Walking/jogging/running - whatever you can handle is best.
OF COURSE weight effects casting! And it's not the pounds - no one is going to have you step on a scale - it's the LOOK. Casting is looking for the image they want to fit the role. The breakdowns are usually very specific as to type - and they will (rarely) consider anyone who doesn't meet their "type" first - and that means before you ever open your mouth.
I don't know what level you are at, but when you get to the bigger leagues, the competition is fierce. You need to know your type and be the best at YOUR type. (The ingenue is rarely busty.)
All that being said - it sounds like your mom is holding the weight loss over your head. She may be doing this with good intentions. We mothers know a lot more about the real world and how tough it can be out there, I'm sure she feels that she is helping you get a better shot at your dreams.
Go to a doctor. Find out what your ideal, healthy weight should be. Work with your mom. Most women I know want to lose a few pounds - you could do this together. She will be a lot more supportive if you are doing the cooking.
Prevention.com has plenty of healthy ideas/diets.
Be your best. Good luck.