Carrot is one of those veggies that is good for everyone. It's tough to imbalance a dosha just from carrots.
Pitta people can enjoy garlic and spicy foods on occasion, it's just when you get sweaty or irritated that you have to totally avoid them. Find your limits and stay within your comfort zone. You can eat absolutely everything, you just have to find the percentages. A pitta person needs a smaller overall percentage of hot, spicy things than other doshas, but they don't have to swear off them altogether.