would I be able to correct the problem by lessening the inflammation by following an anti-infalmmatory diet?
You should start by reading this paper from Nature: Diet, gut microbiota and immune responses. What you need to focus on is alluded to in the title. Neither an anti-inflammatory diet nor treating candida (or any other pathogen) alone is likely to cure your symptoms. Figure 2 really illustrates it well. You’ve already demonstrated what a difference vitamin D levels can make, so this should encourage you to take a multi-faceted approach to combating inflammation.
The best resource I’ve found so far is the blog I already linked to: Cooling Inflammation. Check out the diet at the top and read some of the posts (some of the best info is in the comments) and you should learn a lot. Auto-immune diseases are regularly mentioned, just like in the paper above. One thing that isn’t mentioned much is stress. You can find some good papers on stress and inflammation on Michael Maes’ site. If you don’t have control of your stress response, you’ll struggle to make much progress with anything else.
If you don’t know much about how dietary inflammation works, there are a few articles you should start with on Wiki.
If I understanded correctly, eating complex plant polysacharides (like what?) and 3 fatty acids (are we talking about fish oil here?) are good for lessening the inflammation. Of course, assuming you have corrected your gut flora.
The antinflammation diet looks very worth a try, I will do it.