Immortal NPC encountered on Riften dragon bounty quest

If you have a high enough Illusion skill, you can use the Calm or Fear spells or their higher-level versions to prevent your follower or horse from attacking.

Mods or Console Commands

The mod Better Horses, can set horses to flee at the sight of combat, rather than getting involved and killed. This can be set to all horses except Frost and Shadowmere, or to all horses, including the mentioned two.

The Better Horses mod can also set your horse as 'essential' (i.e. unkillable) or increase your horse's health, preventing or lessening the chances of your horse getting killed. It also has other useful, optional horse-related features.

The mod, Better Stealth AI for Followers, claims to prevent followers from rushing into combat:

This mod improves the stealth AI for followers, so they don't rush into combat before the enemy has fully detected the player. Followers will also unequip torches while sneaking.

The mod Better Followers or Ultimate Follower Overhaul will allow you to set your NPC follower as essential, preventing them from getting killed.

Note that Better Followers and Ultimate Follower Overhaul will work for Permanent followers only and Quest followers may not be affected. Most quest followers are already set to be 'essential' though. Just be careful with those not marked as essential (see who is not set to be 'essential' here).

You could also use the setessential console command to set your horse or follower as unkillable.

It sounds like you're asking about the first dragon you fight, outside of Whiterun, as part of the quest Dragon Rising: you follow Irileth outside Whiterun and upon completing the quest:

The Jarl makes you Thane.

If so, it's supposed to be an introductory dragonslaying encounter: if you followed Irileth around town before heading to the watchtower, you should have a fairly decent posse of guards to help you out.

To be honest, I was still learning how to use the controls on the PlayStation 3 version of the game at this point, and I essentially ran around the watchtower like a chicken with its head cut off. The guards and Irileth will do most of the work. I was a Conjuror build, so I summoned a Flame Atronach for good measure.

After a few minutes, the dragon will die pretty easily, whether you made a significant contribution to the fight or not.