Here's the thing. My brother and I are experimenting with a few friends on starting a post hardcore style band, there's 4 of us and we want to keep it that way. But i'm wondering if we need screaming/rough vocals.

Only issue is (i'm the voocalist) i can't scream. So i'm wondering if a post hardcore band would work without screams?

Any help or examples would be great!

Yep. Most Thursday and Chiodos songs, for example, don't really have any screaming parts. Shouting bits might be effective, though, if you think you can pull that off.
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It doesn't have to have them. The biggest thing is really just the chuging riffs and double bass. and singing about something that might be depressing, but yeah. it could work with only clean vocals. or you could work on your screams and just do them occasionally.
Then I whispered in her ear, fear me dear, for I am Death.

Why are you hiding?
Because the demons from my dreams are everywhere..

Are you arguing with a German guy about how to speak German?