Is it possible for a big boned woman to become skinny?!

Renee it is very possible. You are large boned and you know it. But, that is not a problem.
You did not say your height, weight and measurements so I will just need to talk generally rather than specific. You need to eat well balanced meals cutting your calorie intake- smaller portions.
Start or increase an exercise program- shoot to do it daily. Can you be skinny- I think you can but it would be a large boned female version of being skinny. With large bones you will not look like the model in the picture. But, it is possible if you really work at it to a have a flat stomach. You will not look like that model since she is not large boned. But, any weight you lose will be a bonus for you.
Generally, if you lost weight- it could give you less of a chance to get certain medical problems such as stroke, heart attack or diabetes and certain type of cancers. I am not a doctor so you would need to get a physical examination even if you are perfectly healthy in your opinion.
Once again, you will not look like the model in the picture- but you can get a flat stomach. When will that happen all depends on how much weight do you need to lose. Since you say you are overweight, then you need a medical professional helping to monitor your progress.
Good Luck on your weight loss program. But, do not lose any more weight than you have to.