Hi Maha,
First of all, both cases are pretty much interchangeable in most cases.
값 and 가격 are almost 100% same; meaning "price".
Ex. 값이 얼마에요? = 가격이 얼마에요? = How much is it?
However, 고민 and 걱정 are slightly different.
고민하다 = to think hard in order to solve a problem.
걱정하다 = to be worried (just worried not considering any solution).
Ex. 무슨 고민있어? = 무슨 걱정있어? = Do you have any concern?
그걸 어떻게 해결할지 고민중이야 = I'm thinking how to solve it.
그걸 어떻게 해결할지 걱정이야 = I'm worried over how to solve it.
뭘 살지 고민중이야 = I'm thinking/deciding which one to buy.
Hope it helps.