My daughter is 16. just diagnosed with hypothyroidism. she'll be taking levothyroxine. should we expect an increase in height from treatment?

Hypothyroidism...: There is no guarantee in any medical treatment but one of the issues with hypothyroidism in childhood and adolescence is delayed growth so treatment can definitely help with that. However, especially at her age there are other factors like genetics, bone growth, etc. that can affect her growth rate.

Hard to say: The ability to grow taller will depend on whether or not her growth centers remain open. The growth centers of many women close by 16-17. The hypothyroidism may or may not have influenced this feature depending on how long it was present. An x-ray of her wrist/hand could give a bone maturity/ growth potential estimate. If it reads consistent with age 12, she has plenty of potential, if 16, not.