Cat bites, especially outdoor cat bites, can cause real problems.
I hope you washed it thoroughly and disinfected it.
I wouldn’t give cats fish oil or any oil. Give them cat food.
ANY type of oil can give a cat cirrhosis of the liver and death if given too much, which can be a small amount. This is why weight loss can be such a problem.
I would go to the emergency room at any sign of infection but this might not cause a problem at all.