Could be  a sign of an ammonia problem. Do you have  water test kit? Test for ammonia, nitrite , nitrate, and pH level and post the results here.
How many times do you feed your fish per day and how much? Overfeeding can cause the water to become toxic and result in high ammonia if your filtration is not capable of handling the wastes.
It's hard to know what is causing the problem unless you know what the water quality is like. 
Do you perform partial water changes on a regular basis?

If you don't have a test kit right now, i would perform a 25% water change just to be on the safe side. Make sure you vacumn the gravel too in order to remove food debris  and fish wastes. Most pet stores will do a water test for you if you bring in a sample. Once you know what the different water parameters are , post the results back here.

test water

try feeding him peas

It sounds like your goldfish has a bacterial infection.  Try Melafix (natural antibacterial medication) for a few days and see if you see any improvement.

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You will need to use  antibacterial medication or the fish's condition will probably get worse. I  recommend you try Melafix first. Get some antibacterial medicated food also and feed it to your goldfish if it's willing to eat.

What was the reading for ammonia when you tested it?

You can try Melafix but he may need a oral antibiotic fish food too.
When usig a medicated fish food feed only that for a about a week, twice a day.

There is also Pimafix available to treat fungal and bacterial infections or sores. It is (like Melafix) a natural remedy. Also from API.
Sometimes it helps a lot to treat with both.
Please also check the pH.

ALL THE BEST

OK, red spots are a bacterial infection. Please make sure it is 100% gone before you stop the treatment.
Also keep up with the regular waterchanges, but please make sure that the pH is 7.2-7.6.

If he's dashing arround and then resting, this could be a sign of acidosis, this means he suffers from too acidic water. The water must be alkaline. At the same time he's stressed out.

Please do not turn the filter off, as it filters the waste fish produce.

What is the water temp? How is the pH?

Look at his long tail!
Everyone is right on track with their suggestions, it seems.  Fishie might like a bigger tank, too, as he seems to be pretty big himself.  I also like having real plants in there, but these are just suggestions.