Can I use an appositive phrase after a pronoun? Because some non-native speaker said it was grammatically incorrect. Such as, "I, Deep, am learning the English language."
Your expression is grammatically correct, but unusual.
The use of these appositional phrases is to define and clarify the identity of a noun:
John, the builder, will repair the windows.
Here an apposition is good. If you say "John will repair the windows" its not clear how John is qualified. If you say "The builder will repair the windows" its not clear who "the builder" refers to. But "John, the builder" identifies a particular person and gives relevant information about them.
But "I, Deep" is odd. When you say "I", the other person knows exactly who you are talking about. Adding "I, Deep" adds no information, except your name. But there is no connection between your name and the conclusion "... am learning English". So I am left feeling uncomfortable.
It would be acceptable to say
I, Deep, have a name that is also an English word.
The extra information ("my name is Deep") is relevant to the predicate. But "I, Deep, am learning English" is odd.