I am not sure if this is going to be accepted as a comment or an answer, so apologies in advance and any superuser please feel free to amend it appropriately
I had a condition a month ago when I braked hard, hit a pothole, somersaulted on the road, and my inner tube had a proper burst with cracks on my back tyre. I would say replace your tyre, get something like a 1200 mile puncture-proof tyres (Schwalbe ones are good) for about $40 (guess). Living in a country like UK where you can never rely on the weather, I always get my tyres replaces in case I have a nasty crack. Rain will destroy my tyre anyway, so no point using those clever crack-repairing glues. Speaking of which, for cracks like 2-3 mm you can use those glues to do the job. They are not too bad, considering that you are not riding somewhere really really hot where your tyre pressure is also affected by the temperature. If you are in a place where rain doesn't really affect your riding, you could probably get away with it.
My suggestion is "Replace your tyre if possible" because your safety is not bigger than your cash :)
If your bike was a Road bike (can't remember), definitely replace the tyres. Road bikes are different animal and with about 120 psi on on wheels, you don't want a cracked and damaged tyre supporting the super-pressurised inner tube!