I didn't experience my DD2's reflux quite like you describe, but I thought I'd put some of my experiences out there to see if it is useful in some way.
Basically I would say that I found her reflux 'looked' really different at say 8 weeks than it did at 4 weeks. At 4 weeks it only really presented itself as being chucky, not sleeping during the day (some days not at all) and having trouble getting wind up (and being really uncomfortable before it did come up). By 8 or 9 weeks it presented with a lot more of the 'classic' reflux signs, wet burps that made her scream, screaming during feeds and breast refusal, was uncomfortable and unsettled a lot of the time, wanting to feed often (for comfort) etc.

From what I've read it can often be like this, not really showing the classic signs until 7 or 8 weeks old, I read many stories of babies who'd started medication at 9-12 weeks, I assume because it took a few weeks for their reflux to present with the classic signs. I've heard people say diagnosing reflux in babies under 6 weeks is tricky because the signs at that age aren't that distinctive and can easily be confused with other things like hunger, being overtired, colic etc. where as later they are more distinctive.

So I guess there is a chance that coincidentally your DS's relux has kicked in (or looked more obvious) at a similar time to the immunisations? I remember DD2 being really cranky for about a week after her 2 months immunisations (which were at about 9 weeks) but her more obvious reflux stuff definitely appeared before then.