"Dream within a dream"
No. It's correct with 의. It's not very easy to explain, but 'X 속의 Y' means 'Y that belongs to the inside of X' or simplier 'Y which is inside X'
내 마음 속의 생각 - a thought in my mind
'마음 속' - is a single entity in this case, the 'inside part of my mind'
의 is a possesion indicator. 생각 - thought
A thought belongs to the insideness of my mind. Less literally: The thought is in my mind.
Note that it's not a proper sentence since it lacks a verb. It's just a word structure.