Frances,
HbH means 3 out of 4 alpha genes are deleted. The child gets 2 of these genes from each parent, so for it to be HbH, one parent would have to be an alpha thal with 2 genes deleted. The other parent would most likely be a one gene silent carrier, and probably be unaware that they are a carrier. Alpha thal is not easy to determine in adults without doing DNA testing. If the child does have HbH, both parents are carriers. Alpha carriers quite often have few if any symptoms and don't know they are carriers.
Breastfeeding is best and does help the immune system greatly. You should take folate because you are a woman of child bearing age. Right now, the baby's Hb is good, so it isn't immediately urgent, but it will be if the child does have HbH.
Gallbladder problems are not uncommon in thal minors because there is a higher than normal turnover of red blood cells and this creates bilirubin, which can lead to gallstones.
Until the DNA test comes back, you won't know for sure. Up to 15% Hb barts is usually 2 gene carrier status. Over 20% is almost certainly HbH. In between 15-20 requires further testing.