Hi, I'm stunned that your parents would call you chubby! At 5ft 6 you are almost certainly underweight at 110 lbs. You can find BMI calculators on the web if you want to check it out. I am 5 ft 3 and weigh 132 lbs, I come out as normal weight on the BMI calc. Sounds like your dad is very underweight too. I just put your details into a calc and you do come out as underweight. I have included a link below if you want to check. Don't be bullied into losing dieting, you'll make yourself ill. You know yourself that you feel skinny. I agree with your brother.
http://www.halls.md/body-mass-index/av.htm
Good luck
You are actually considerably underweight and I'm shocked that your parents would consider you "chubby"....... Your father could be healthy at 95 pounds, if he has no fat on him at all - but I'd guess he looks pretty scrawny........
I copied just a section of a height/weight chart - for your height:
Height Small Frame Medium Frame Large Frame
5'6" 120-133 130-144 140-159
You are not overweight and if you are comfortable with the way you look, you'll be fine. If you become too much more underweight, you won't be healthy........and you don't want your parent's attitudes to cause you to end up with an eating disorder.
I'd hate to hear what they had to say about ME ------------- lol.........