As for the question in your title, yes, they are the same. Sometimes it's just a fancy way to express the same thing. 向 is a little bit fancier, or poetic, while 对 is widely used in plain texts or conversations. In some dialects 跟 can also be used, they are all the same.
It's like when you write a poem in English, you just need a different word than daily conversations. And 傷痛向誰說 feels like a sentence from a song's lyrics or modern poem, because 傷痛 is rarely used in daily conversations.
As for 傷痛說向誰, @dan's answer is pretty clear. Just to add a little bit, 傷痛說向誰 is valid and meaningful in poetics, and is even more 'poetic' then 傷痛向誰說.
For example, the following ancient poem use similar grammar:
Many times poems and song lyrics simply don't follow the 'daily' grammar strictly because they need to rhyme， simple as that. Also, the ancient Chinese had a different 'convention' than the current one, and in poems it's pretty common to mix them. Some of the 'ancient' grammar are still in use but only in limited circumstances. Things can get even more complicated regarding dialects, They vary so much that you can call them different languages.
If you listen to Chinese pop songs you'll find some lyrics that look really weird in grammar, sometimes the artists do it deliberately to express an idea or a feeling, most of the time they just mess with the order of the words to rhyme. And occasionally, if the writer is sub-par, they just write meaningless sentences and call it art. It's subtle, but keep reading and writing and you'll feel the difference.