From the LDOCE:
be about to do something
if someone is about to do something, or if something is about to happen, they will do it or it will happen very soon
- We were just about to leave when Jerry arrived.
- Work was about to start on a new factory building.
In this idiom, to is the infinitive marker, and it always has to be followed by the infinitive form of the verb. Because this isn't the preposition to, it can't take the -ing form of a verb as a complement, so your example is ungrammatical:
**I already was about to going class tomorrow morning. (very ungrammatical)
If we replace it with the infinitive, it's better:
*I already was about to go class tomorrow morning. (ungrammatical)
But it's still ungrammatical because of another problem. The verb go can take a preposition phrase as a locative complement, but class isn't a preposition phrase, it's a noun. We need to indicate a destination with the preposition phrase to class:
I already was about to go to class tomorrow morning. (OK)
In this sentence, the first to is the infinitive marker introducing go, while the second to is a preposition marking a location as a destination. You need both in this sentence.
I already was about to go to the class tomorrow morning. (OK)
Your last example added the word the. This is also grammatical, but whether it's appropriate depends on whether the context licenses it. Without a special context, most speakers would probably use class without a determiner.
In this answer:
- The * symbol indicates that an utterance is ungrammatical.
- The ** symbol indicates that an utterance is ungrammatical for multiple reasons.