handling collision with two objects of the same tag

Why not use a script on the bullet objects with the OnTrigger function? Say your player has a script called "Health", and you bullet has a script called "Bullet" for examples sake.

 //Health.cs
 
 using UnityEngine;
 using System.Collections;
 
 public class Health : MonoBehaviour
 {
     public int health = 100;
     
     void Update()
     {
         if(health <= 0)
         {
             //Code for dying
         }
     } 
 }

Then your bullet script could call the component Health on your player, and decrease the health when it hits.

 //Bullet.cs
 
 using UnityEngine;
 using System.Collections;
 
 public class Bullet : MonoBehaviour
 {
     int damage = 10;
     
     void OnTriggerEnter(Collider other)
     {
         if(other.collider.tag == "Player")
         {
             other.collider.gameObject.GetComponent<Health>().health -= damage;
         }
     }
 }
 

NOTE: If your bullets are rigidbodies, be sure to set their collision detection to Continuous Dynamic. Any rigidbodies these bullets hit should be set to Continuous. Also, disabling gravity on the bullets will help them fly, just in case you had other issues.