Filter Tags for current users

This is a possible way of doing this.
Whenever a new term is created, you execute the following code.

This code saves the current user_id as the term author, which should allow you to filter by user_id when fetching terms.

add_action( 'created_term', 'filter_user_specific_term', 10, 3 );

function filter_user($term_id, $tt_id, $taxonomy){
    if( $taxonomy == "my_custom_taxonomy"){
        if (isset($term_id)) {
            add_term_meta ($term_id, "author", get_current_user_id());
        }
    }
}

To get the term list, according to current user:

$terms = get_terms( array(
    'taxonomy' => 'my_custom_taxonomy',
    'meta_key' => 'author',
    'meta_value' => get_current_user_id() ) );

I didn’t test this code but should be a good start point for doing what you want.