You can patch the inside of a tire. That is the correct way to do it. The only problem is that if the patch is too big it can throw the tire out of balance. Most automotive tire shops wont have the correct equipment to mount and dismount motorcycles tires, so they may scratch your rim. If you are concerned about that, you may ask around or go to a good motorcycle shop.
For a new tire in Chihuahua try these guys. There are probably the biggest shop in Chihuahua and deal with big bikes not pizza delivery bikes.
One of the best rides in Mexico is from Creel down to Parral through Guachochi. You are not too far away. If you get your tire fixed, It's almost worth back tracking from Chihuahua city for.
If you are heading south to Durango, a shop here has a Metzler 19" front for 3,500 pesos and should have a Metzler 17' rear in tomorrow for 4,000 pesos. Shinkos are in stock and cost 2,000 for front and 2,500 for rear. Maybe that will help you decide what to do.