As I explained in your previous post, 'home' is an adverb, like 'here' and 'there', so you don't need to use the preposition 'to'.
'I'm heading home' is fine as it is.
For other places, such as school or work, or names of locations, you need to use a preposition to indicate movement.
I'm heading to school.
I'm heading to the airport.
I'm heading to London.
You can also use other prepositions, such as 'towards' or 'for', to show movement.
As for the verb form, the standard form which is acceptable anywhere, is 'I am heading home'. American English also uses the rather more informal variant, 'headed home.'