I'd say that it is too early to jump the proverbial gun, and send it to a gunsmith.
You haven't given us much information. If this happened with a gun that I owned, I'd first be looking carefully at the indentations on the primers. It takes a solid and consistent hit on the center of the primer to have the shell fire reliably. I would also observe whether the hammers move freely during cocking and firing, and whether the cocking force (or mainspring tension) felt normal and equal for both locks.
Then, considering that the problem started with one barrel, and soon began to misfire with the second barrel, I'd start to suspect a possible problem with your ammunition. It will be a whole lot cheaper and easier for you to figure this out by trying the gun with another brand or lot of ammo, rather than immediately concluding that the firing mechanism in both locks suddenly quit working correctly. Locks sometimes fail. Rarely do they both fail in the same round of skeet, unless the ammo is bad, or something like congealed lube in the locks has reduced the force of the hammers striking the firing pins.
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