Well, yes, tee tree oil will be fine and in most cases, it will just do a good job for your eyes. And according to some researches, tea tree oil contains a cosmetic product and purcelin oil that can help improve the appearance of scars, stretch marks. And so there are many people who applying tea tree oil to treat black eyes, which is related to injury occurring on eyes. Also, puffy eyes and dark circles under eyes can be treated with tea tree oil too. On the other hand, you should just keep using tea tree oil, and only in that way will it be effective on your eyes.