koNdu thirindhEnO thiruvadiyaip pOlE
The term “thiruvadi” refers to the Vehicle Mount (Vahana) of Lord Vishnu. Both Garuda (periya thiruvadi) and Hanuman (siriya thiruvadi) are referred here. They got this name because they both perform the service of carrying the Lord, wherever and whenever he wants. Just as Adisesha does various services, so too Garuda and Hanuman acts as the Lord's friend, His servant, His conveyance, His seat, His flag, His umbrella, etc.
In Hindu Mythology, Garuda is a divine eagle-like sun bird and the king of birds. The Shatapatha Brahmana embedded inside the Yajurveda text mentions Garuda as the personification of courage. He is a powerful creature in the epics, whose wing flapping can stop the spinning of heaven, earth and hell. Azhwars refer many times to the fact that the Lord rides Garuda and performs various acts.
Hanuman is referred as the vehicle mount of Lord Rama, an avatar of Lord Vishnu. He symbolizes the human excellences of inner self-control, faith and service to a cause, hidden behind the first impressions of a being who looks like a monkey. In the great Indian epic Ramayan, Hanuman carried Lord Rama and Lakshmana on a few occasions. When they first arrived to meet Sugriva, after ensuring that they are not sent by King Vaali, Hanuman carried Lord Rama and Lakshmana on his shoulders to Sugriva. Later when Lord Rama and Lakshmana waged a war against Ravana, he carried them again on his shoulders so that they do not have to stand on the ground and fight.
Thirukkolur Ammal is asking "Did I carry the Lord on my shoulders with affection like Garuda and Hanuman?"