Cushing was suspended for four games without pay last week for violating the NFL's drug policy. His appeal was denied.
Cushing confirmed he tested positive for HCG, a fertility drug that is on the league's banned substance list.
"The question of how it got into my body is still unclear," he said. "It's something that I'm very personally concerned about, just the fact that how it's there and what's going to determine it from happening again, and that's something we're going to have to medically investigate."
He said that after failing the test, he was told HCG can get in your body from injecting it or because of tumors. He said this information led him to believe he had tumors. He did not say what kind of tumors.
"I personally know I'm not injecting myself with anything," he said. "I played the whole season thinking this could not only be my last season, but my last year."
Cushing added he is concerned about his health and plans to undergo tests to see "how this got into my body" and to try to make sure it doesn't happen again.
In a statement Saturday, Cushing said the test indicated "the presence of a non-steroidal banned substance." He said he took the test in September and was notified of the results in October.
Dr. Gary Wadler, who leads the committee that determines the World Anti-Doping Agency's banned-substances list, said there have been cases of malignant testicular tumors producing HCG. Still, those cases are "extremely rare."
"If he had a tumor that produced HCG, he wouldn't be playing football," Wadler said of Cushing. "He would be under treatment for a malignant tumor."
Wadler also noted if Cushing tested positive once because of such a tumor, HCG levels would be consistently elevated and he would continue to have positive tests.
"Malignant testicular tumors producing HCG are rather lethal," Wadler said. "It is a fairly aggressive tumor and you're not playing in the NFL with one."
Cushing retained The Associated Press NFL Defensive Rookie of the Year award in a revote Wednesday prompted by the penalty. He won the original balloting in January with 39 votes out of 50 from a nationwide panel of sports writers and broadcasters who cover the NFL. This time, he got 18 votes to 13 for Buffalo's Jairus Byrd and 12 for Green Bay's Clay Matthews III.
He is offended that some in the media have called for him to give up the award.
"Why? I know I didn't do anything," he said. "I earned that award. I did everything I could. I was disappointed with the revote, but I have to respect the process again. But, no, I would never. I know what I did."
Fellow Texans linebacker DeMeco Ryans spoke on behalf of Cushing's teammates after Cushing spoke. Ryans was pleased Cushing retained the award that he also won after his rookie season in 2006.
"It was very important for him, it was a huge award and I was happy that he got it again and he deserved it again," he said. "He was the best rookie defensive player there was and he went out and proved that. Coming in this year after he's gone those four games I don't see any drop-off in what Cushing is going to bring to us. You'll see that same level of play."
Cushing read from a statement before taking questions. Coach Gary Kubiak and general manager Rick Smith sat nearby; neither commented before leaving.
Cushing said he was sorry he had become a distraction for the team.
"That's the thing I'm regretful about, is the fact that it's taken away from the Texans organization," Cushing said. "That's not going to change our goal. That's not going to change our achievements. We're going full speed ahead toward a championship."
The Texans have never been to the playoffs, but finished 9-7 for their first winning season in 2009, with Cushing's help on a young defense.