You have a lot of assumptions in your argument, very few of which you have actually mentioned, and even fewer justified.

Of the assumptions that you do make, I would seriously argue about 2, and 3 seems to provide a very limited definition of prostitution.

Also, you are trying to figure out whether something is moral, without actually defining what you mean by moral, and the couple of examples you mention seem extremely cherry picked to justify your conclusion.

Really weak argument there.