I feel cold very easily. Am I underweight?

Nope, you're smack in the middle of healthy. Some of us just freeze more easily than others. As long as circulation is good and you're in good health that's probably just the way you are. If you're sedentary you can do regular exercise and this will improve both your circulation and your metabolism. If you've recently moved from somewhere warmer it can take a while to acclimatise. The last country I lived in was technically colder in the winter but where I live now has much higher humidity. I couldn't believe how cold I was the first year here. It took me about three to fully acclimatise but now that I see visitors around me all bundled up and some ask me to turn on the heating I know that I have adjusted.

No, even if you weight ten lbs less you wouldn't be underweight. This is a good weight for your height. You're cold because you probably have a problem with your circulation, hormonal imbalance, lack vital nutrients, are tired, etc... see a doctor.

I have calculated your Body Mass Index (BMI) and it comes to ~19.5. That is completely normal and acceptable for a young female. The fashion model industry has passed a law/rule that will not allow a young woman to walk the runway with a BMI less than 18.5. About one third of the girls were disqualified until they gained a few pounds when that rule went into effect.

As far as being cold all the time, that is what boys are for.