Place chicken in the Instant Pot and add chicken broth, jalapeno juice, pickled jalapenos, sliced jalapeno, Ranch seasoning, and pepper.
Place lid on and set to Pressure Cook or "Manual" for 15 minutes.
Do a quick pressure release. Pour all the liquid into a large glass measuring cup. Pour 1 cup back into the Instant Pot. (Save the rest in case you need to thin the sauce some.)
Add the cream cheese and cheddar cheese. Set the lid back on and let it sit for 5 minutes to melt the cheese. Stir well.
Shred the chicken. You can either shred it in the pot or remove it to a bowl or cutting board.