I'm not a doctor but I don't see how blood work would detect any problems with sulfate as the usual reported effect of sulfate on persons exposed to higher levels of it than that to which they are accustomed is the 'quick step'. EPA has a secondary MCL for it of 250 mg/L but that is based on taste and smell. They have studied the question of whether there are any adverse effects of it on certain populations and concluded that there aren't though there have been anecdotal reports of sulfate induced trots in infants given high sulfate water for the first time.
That aside, sulfate really has no role in brewing unless you happen to be addicted to the peculiar combination of British hop varieties and high sulfate water. Many people (including most on the continent) prefer that their beers be made with low sulfate water as the sharpness/harshness that sulfate lends to hops bitterness is not generally found desirable. It has a particularly unfortunate effect on noble hops destroying the 'fine' quality to those varieties' bitterness. There are those, however, who like the effects of sulfate and find that beers made without it are 'lifeless'.
The obvious thing for you to do is install an RO system and drink exclusively from that to see if your problem goes away. If it does then sulfate may indeed not agree with you and you can, henceforth, brew exclusively with RO water using only calcium chloride to set the mineral content at a reasonable level.