It looks like fungus to me, but I am terrible at interpreting flat pictures. :happy:
Assuming it is fungus, as long as it doesn't spread, it will probably heal on its own, given good water conditions.
Check all of your water parameters. If nitrates are above 40 ppm, start doing water changes until it is well below that. It has been reported (and I have seen it myself) that high nitrates in the water are associated with more minor fungus infections. (If ammonia or nitrites are elevated, take care of that, ASAP as appropriate.)
Are there tank mates or anything in there that might have injured her gills for the fungus to take hold? If there are sharp or rough edges or places that could trap her gills, you should take care of that.
With respect to "fat", if it is eggs, she will not lay (and should just reabsorb them) unless there is a male to fertilize them