In both instances, the flying bug was acting as a divine messenger and that is the reason you noticed and had the thought to make the connection, you were being impulsed at the same time to consider this possibility, so it was a divine communication of a dual nature—one coming from within as a direct communication from the higher self impulsed by Creator, and one coming from the environment on the part of the flying insect responding to a divine instruction to fly in the way it did and to hover and seemingly look into your eyes. This was simply a way to get your attention and reinforce the interior message that Creator was saying, “Hello,” and in the bargain, rewarding you for paying attention to the messages you have heard from the channeling work and taking seriously the operation of reaching out to the divine as a healer and doing such fine work.
Insects can be pressed into duty in the same way as birds, and this is often easier to achieve. It is only that birds are more likely to be seen as friendly and a happy event if they come close to a person than is the case with bugs, which are often pests, and many people will react quite negatively to close proximity by an insect, just out of their conditioned response wanting to shoo such insects away, so this is factored in when the divine realm selects a way to create a message opportunity. They will not put a snake in your bed if you fear snakes. If you love reptiles, they might send one your way because that is something of a personal nature that is meaningful, but only to a very few. It is the unexpected which is used, time and again, as an element in divine communication, in order to have it be noticed. A mundane event occurring often on its own would not serve such a purpose and that is why having an insect seem to take an interest in a person but not in a threatening or invasive way, fills the bill, because it is unexpected to seemingly have a kind of intelligence in how it is behaving and seemingly to be holding a thought about the person. This is quite unlike insects, which often bump into humans as though they are simply an object with no greater significance to them. Divine messages are sacred because they honor the divinity of the recipient however they are delivered.