Can you see the rusty color without the use of a flahlight or camera flash? If so, it's probably his natural coloring.
Bettas can go several weeks without eatting. I wouldn't worry about him starving but the fact that he is not eating is worrisome.
Before you treat your fish for everything under the sun, check the water chemistry. Toxic levels of Ammonia, Nitrites and Nitrates are extremely harmful and weaken your betta's immune system resulting in illness. Many petstores will test your water for free. Liquid tests are much more accurate than strip tests.
•If your fish look like they are lethargic, gasping for air or are swimming head down do a water change immediately because they probably have nitrate, nitrite, or ammonia poisoning. Do not use chemicals to remove them as they are ineffective. Prime does remove nitrites/nitrates but it is still most effective to do a water change.
•Extreme pH variation can also cause illness. Sand and porous rocks like sandstone or lava rock make water more basic (>7.0) while Indian almond leaves, peat moss and oak leaves make the water more acidic (<7.0).
•Are there chlorinates in the water? Did you forget to add the water conditioner? If so, quickly add your water conditioner!!
•Many issues can be cured by a simple water change so it should be the first thing you try.
•Symptoms: Can be found by shining a flashlight on your betta. If it looks like it is covered in fine gold of rust colored dust then it has velvet. Clamped Fins, no appetite, darting/rubbing, loss of color, lethargic
•Treatment: It is very contagious so you should treat the entire tank. Treat as you would treat Ick. PP is also my favorite for treating Velvet.
However, keep in mind that some bettas have a natural goldish or rust coloring. Normally the only way to spot velvet is by shinning a light on the fish and it will be covered with gold flakes. To me, it looks like they are covered in pollen.
Are you using water conditioner? and do you know what the ammonia level is? I'm wondering if your tap has ammonia in it.