Will going slightly over my calorie limit affect my diet?

I wouldn't worry and overstress about one day going over your calorie deficit, a lot of people incorporate 'cheat days' into their cuts anyway which is perfectly normal and makes things less stressful.

You sound like you're doing really well so keep it up and keep consistent, eating above your deficit every now and again isn't going to impact your progress everyone does it otherwise losing weight would be miserable! Plus you've got 7 days in a week and eating healthier for 6 of them is an incredible achievement as it is, that one day isn't going to negate your progress. 2000 calories is the recommended AVERAGE for adults anyway, that will differ with every person and everyone has different intakes to maintain weight. It's a healthy amount of calories to consume anyway, so again I wouldn't overstress.

So I've been dieting and exercising since New Year's Day, today is the first time since then I've eaten something unhealthy (a KFC) and the second time I skipped the gym. I definitely ate more than 1500 calories today (which you're supposed to eat when dieting) and might have ate more than 2000 (which you're supposed to eat daily to maintain your weight). If I did eat more than that am I going to put weight on? I'm so ****ed off with myself, I was doing quite well.

I guess you're right, but I've tried dieting/exercising before and gave up because the food was disgusting and the gym too hard, so I don't want to do that again. I promised myself I wouldn't eat rubbish except for birthdays/Christmas etc or miss the gym unless something important came up, so I am quite annoyed with myself.