Yes you can bring fish oil on the plane in your carry on luggage as long as the fish oil is in the original container and sealed up.
I've taken fish oil pills on the plane in my carry on luggage in my purse and it's never been a problem and you can take other vitamins, supplements and your other medications in your carry on luggage through the security and bring it on the plane with you.
It's actually better to bring the fish oil and other medications on the plane through your carry on luggage in case your other luggage gets lost.
I have had checked baggage lost for awhile before and it's better that I had my medication and supplements in my carry on luggage.