Place chicken, chicken stock, tomatoes, green chilis, chipotle chilis, adobo, lime, garlic, salt, and pepper in the Instant Pot.Close the lid and switch the valve to "Sealing."Push the "Pressure Cook" button and adjust the cooking time to 20 minutes. After the cooking is complete, let the pressure naturally release for 5 minutes, then manually release the pressure by switching the valve to "Venting."
Once the pressure is released and the red floating valve goes down, press the "Cancel" button. Remove the lid then remove the chipotle chilis from the soup and discard.
Remove the chicken using tongs and place the chicken breasts on a clean plate to shred. Shred the chicken using 2 forks. Add the block of cream cheese to the soup.Stir or whisk the cream cheese until fully melted and incorporated. Once the cream cheese is fully mixed, add the chicken back into the Instant Pot. Serve hot with shredded cheese, cilantro, and a squeeze of lime juice if desired. Reheat the soup by pressing the "Keep Warm" button and serve when ready. Store leftovers in the refrigerator in an airtight container for 4-5 days.