This has been debated since the late 70s. I don't accept the binary of pro/anti-pornography, or the claim of sexual liberals that I'm trying to violate the first amendment.
The civil legislation proposed and knocked down in the 80s framed pornography as a violation of civil rights. I think that legislation, revised to include the three-pronged exclusion for art/education, could still guide us now, though our powers against the corporate state (including international brokers of vicious pornography) are even more abridged now than they were in the 80s.
Most pornography is a harm, either committed in the creation or committed in its usage as public harassment or the training manual for sexual abuse, and those actions are not protected speech. They are actions. There are plenty of civil harms that could be reframed as speech by the defendants, but no one takes that seriously. If a gang beats up an immigrant and calls him a wet***k, and films it, that would be evidence used in a court of law for a hate crime. If the group sold the film, its profits would probably be recoverable by the victim. Making the harm a tort isn't prior restraint. People can shout fire in a crowded theatre. We don't restrain them in advance. But it's legally actionable (as a crime and civilly, in that case) and if that has a chilling effect, so be it.
I really recommend you get ahold of MacKinnon's short book, Only Words. If that's too dense (and it can be) then Dworkin (google Nikki Craft's site or get Letters from a War Zone) and Stoltenberg (Refusing to be a Man) have more powerful visceral arguments.