Infant Reflux & Sweating (Parents & Child)

I have an 11-week old baby who is suffering from reflux -- he is a happy, easy baby, who spits up after every feeding (breastfed exclusively), sometimes in very large quanitities. It is worse at night and/or if he is around people who are stressed.
I am going to try the silica remedy listed on other threads, but I am wondreing if it is related to his sweating:
In the first momoents of feeding, his hairline and eyebrows break out in a sweat. Also if he cries at all, he sweats. With contnued crying (which is rare, he almost never cries) he sweats full body. His father apparently did the same as a baby and still sweats very easily and excessively, full body, when doing any sort of movement or in temperatures over 65F. The father is 5'10', 250LBs, mostly muscle, with all the extra flab around his abdomen, Irish/scottish and a beer drinker.
Myself, it is the opposite problem: I don't sweat anywhere except under my armpits, even during extreme heat or exercise, but I have excessive sweat problems under my armpits, and am of Spanish & French Extraction. I can sweat through sweaters in an instant. It generally happens only when around other people or when I am nervous. I have a fear of public speaking in front of people I don't know, and am tall and average weight (5'8', 150LBs)

What is the best remedy for my baby's reflux that will not worsen these other symptoms?
He is:
11 weeks old
Gaining weight very well
Normal breastfed infant stools (yellow, mustardy)
full head of dark hair, dark eyes
happy, alert, never fussy
likes to be held
will only sleep on stomach
in Connecticut US
sleeps well, and through the night
sweats easily
sweats when cries/eats on hairline, eyebrows, eyelids
prone to heat rash where he sweats
had diaper rash at 3 weeks (better now)
Reflux -- spits up with burps after feedings, sometimes vomits
Breastfed exclusively. Mother had very overabundant milk supply & forceful let-down, which was adjusted down by sage & peppermint tea

Thank you so much for any help. My main concern is the baby's reflux, his & my own sweating is secondary.