Mine was sent Feb 22. As of April 14, I got the same website response as you. I called my CPA and he confirmed it was filed Feb 22.
I *just* checked the IRS website again, and it now shows that my return has been received, accepted and the check will be issued next week.
I also read some article a week+ ago that mentioned the IRS is way, way behind on processing.
Mine was filed electronically, but without a direct deposit option.
I think they're just S-L-O-W if you file the paper-way.
I'd wager you're OK!
-Pidge