A leave in hair treatment such as "It's a 10" can give you the moisture it needs while protecting your hair from further damage. I would follow up with a smoothing serum after the hair is dry to protect the hair from frizz and give it a silky smooth finish and shine. I personally like Glass made by Redken and Glaze Haze made by Bed Head.
Use caution when putting a smoothing serum on your hair a tiny bit goes a long way!
Ultimately, trimming off all the burnt hair is the ideal approach to your dilemma.
Hope this helps you