Should I reopen this hand?
If partner's double of 3C would have been negative, double here is not for penalty. It shows a hand with shortness in the overcalled suit and tolerance for responder's bids. Your plan here is to double and correct partner's potential 3D to 3H. Partner may have passed with a hand like Qxx x AJxx KJTxx, which might make 3NT but also probably beats 3CX by 3 tricks or more, in which case you need to double to protect partner's holding.

If partner's double of 3C would have been for penalty, then your choice is between pass and 3H. Even though partner needs very little for you to make 3H (essentially Kx in hearts and Qxx in spades is enough to give you chances), you could easily go down 3, which is a terrible risk. Therefore, pass is probably the best choice.