In 2009, Carter risked his life to save an injured soldier and to resupply ammunition to his out-numbered comrades during intense fighting with the Taliban.
Obama says carter displayed the essence of true heroism.
"Ty said he was hoping to take his children around Washington to show them the sights and the history," Obama said. "But Jayden, Madison, if you want to know what makes our country truly great, if you want to know what a true American hero looks like, you don't have to look too far. You just have to look at your dad."
Carter now suffers from post-traumatic stress disorder and after the ceremony, he encouraged the public to learn more about the "invisible wounds of war."
"Know that a soldier or veteran suffering from post-traumatic stress is one of the most passionate dedicated men or women you will ever meet," he said. "Know that they are not damaged, they are simply burdened with living when others did not. Know that they -- we are not defeated -- never defeated. We are resilient and will emerge stronger over time."
Carter's courageous statement about his personal struggle is an inspiration to the thousands of soldiers who come home from war zones only to battle PTSD.
Oakley's Ryan Mason served to one tour with the Marines in Afghanistan and three in Iraq. Like so many young veterans, the 25-year-old says he has symptoms of PTSD.
"For me it's thunder; thunder sounds way too much like artillery landing and that thunder will send me running, it will," Mason said.
Mason is not alone. The U.S. Department of Veterans Affairs estimate as many as 30 percent of veterans returning from Iraq and Afghanistan will have symptoms of PTSD.
Dr. Keith Armstrong with San Francisco's Veterans Medical Center says Carter's being hailed as a hero might actually intensify his PTSD.
"For instance, it might bring up 'why did I survive and why did some of the folks I was trying to help didn't make it' and 'could I have done anything to prevent that,'" Armstrong said.
But for Mason and his fellow Marine veteran Robert Baskins of Antioch, having someone like Carter talk about his struggles helps them.
"Every combat veteran would know he's gone through a lot receiving the Medal of Honor; so coming out with it will probably help a lot more people come out with it," Baskins said.
Armstrong says putting too much pressure on returning veterans to quickly adapt to life at home and get over their combat experiences can often make their homecoming even more difficult.