I plan to travel to America a month after I've travelled to Iraq .... will this cause me a problem on arrival in America?
Neither USA nor UN impose sanctions on Iraq anymore, nor are the countries at (quasi-)war, which means that there should be no problem for you to travel to the US with an Iraqi visa in your passport.
Be prepared to explain what you were doing in Iraq, though, and make sure that the answers doesn't include stuff like "killing infidels". Visiting family, or archeological sites, or being there on business should be good reasons.
If you're really worried, consider contacting the nearest US embassy or consulate for more information (and bring a printout of the email with you, just in case).