Is there any way to shout more often?
An Amulet of Talos will reduce the time between shouts by 20%. I believe this stacks with the +20% to shout recovery from shrines to Talos, which will knock a whopping 40% off your recovery time.
Sadly, you cannot disenchant the amulet and learn to make your own +Shout Recovery items.
Also the dragon mask Morokei (requires unofficial bugfix patch) adds another 20% getting you to 60%.
The help given above - amulet and blessing of Talos plus the dragon mask Morokei for 20% reduction each.
The best reduction can be gotten if you do not use your fire breath on Paarthurnax during the quest "The throat of the world". Until you continue the quest (breath fire on the old dragon) all your shouts will have a cooldown of approx 5 secs.
There is also the Amulet of Talos, which reduces shout cooldown by 20%. One is found on the body of Roggvir who is executed the first time you visit Solitude, but you might lose it due to a quest.
Another occasion where you might find this Amulet is when you exit Ironbind Barrow after clearing it, look around at the mountain peak. It should be lying around on a statue between two chests.
A third one is Ogmund's Amulet Of Talos in Understone Keep, Markarth, The Reach. This is one of the items you can use to blackmail Ogmund during the Miscellaneous Objective 'Triumph Over Talos'.
This forum thread shows similar behavior; are you already wearing the Amulet of Talos by accident? It might be the case that if you wear the Amulet of Talos, that the Blessing of Talos no longer has effect to prevent you from stacking both. Given that they list a reducement, it sounds like a bug...