Don't feel bad. The research into gut flora is still developing. Make sure to give him a course of probiotics once he's off them.
DD had ABs at birth, didn't need them at all for a couple of years then had so many I lost count until the tonsils came out. I would give her inner health and she's strong like an ox now, rarely sick, no allergies, no asthma (both run in our families).
I would think there would be a definite correlation between ABs and athsma. To use my nephew as an example, if he gets a respiratory infection it triggers his athsma. So his parents need to be vigilant in ensuring treating any viruses that develop into a bacterial infection as 'riding it out' could see him in hospital from his athsma. Do as a statistic, he probably has had more ABs than most non-athsmatic kids his age.