Heat olive oil in Instant Pot on sauté mode. Add diced onion, pepper, and jalapeño. Sauté until softened, about 5 minutes. Add garlic and sauté for another 30 seconds. Turn off pot.
Add chicken, potatoes, cilantro, corn, lime juice, 1/2 teaspoon salt, black pepper, and chicken broth. Stir well.
Cook on high pressure for 10 minutes. Let natural release for 10 minutes.
Remove chicken from pot and shred. Do NOT yet return shredded chicken to pot.
In a small bowl, whisk the eggs together.
Remove about 1 cup of soup from the Instant Pot and very slowly pour it into the eggs while constantly whisking. Then, very slowly, pour the egg mixture back into the pot, again while constantly whisking.
Stir in shredded chicken.
Serve with cheddar cheese and sour cream if desired.