Dogs growling at each other usually isn't a big deal. Just keep the leashes short enough so they can't make physical contact and all will be well.
When my dogs get out of hand (they hate certain breeds and the little one hates little dogs) I make mine sit quietly. When they are calm, we move on. If another dog looks like it won't be controlled, I move my dogs out of the way. Granted, we have lawns and driveways for me to move onto should that be necessary around here.
The biggest thing you did wrong which requires more practice on your part is how you carried your dog. Practice grabbing items and holding them with your left hand so that you can still use your gun in an emergency. Once you do that enough, then you will do it reflexively. Problem solved.