No, you're definitely not too old to start pitching -- and you're not too old do it on a competitive basis. However, you should be realistic about your goals and what you hope to accomplish.
There are literally hundreds of adult-league baseball teams across the country foaming at the mouth for good pitchers. (Everyone wants to swing for the fences, not pitch.) You could start there. Contact your local recreation league for details. If you're serious about your pitching, you may have to put up with some guys who are only out there for a few drinks and some laughs with the guys. However, that could be a good proving ground. You know, see if you have some success there.
There are advanced competitive adult baseball leagues and semi-pro and non-affiliated pro teams, too. (A lot, actually!) That may be the next step if you're able to really string together some good outings in the adult league, you're throwing hard and commanding your off-speed pitches (i.e. you're able to throw an off-speed pitch for a strike with conviction to a batter in a full-count situation).
But with semi-pro and non-affiliated pro ball, your competition is very stiff. You'll be competing against really quality pitchers who are either 1) just under the draft bubble (good but not quite good enough), or 2) on their way out of a career in professional baseball, but still hanging on to the dream.
It's highly unlikely you'll get a shot to pitch professionally. Though there are exceptions (think Disney's "The Rookie" here) most pitchers who've gone undrafted at 22 or 23 years old -- and have not played organized baseball for a year (or a couple of years) -- have little to no chance to get picked up by a big league team.