Oh, Adip, I feel for you! This sounds like my DD, who, although she is often cranky now, was definitely worse around the 5-7 week mark.
First of all - the crazy crying spells became most noticeable at around week 4-5, and usually in the evenings, so we thought it must be colic, although she did cry a fair amount during the day, too (though more grizzling than actual screaming). She's never done the classic colic thing of pulling her knees up to her tummy, though, but has always arched her back, which I didn't know was a symptom of reflux until now. The awful crying isn't/wasn't every day, but often enough to make things very difficult. I think because we learned tricks to stop her crying - eg. driving around in the car, the sling (which doesn't work when she's really hysterical) and comfort breastfeeding (ie. when she's not actually hungry) - she's cried less, but only because of these things (and they often take a while to work - we can drive around for half an hour or longer before she starts to calm down).
On the feeding front - I have mix-fed her since week 2 as we had loads of problems with breastfeeding and she too would feed for hours on end and especially at night I found this really hard to cope with as I just wasn't getting any sleep. So now she gets breastfed (luckily it's got easier) during the day, with formula top-ups, and bottle-fed at night. Luckily she's never screamed at night (or only briefly), but is very grizzly in her sleep from the early morning onwards.
I too wonder if reflux is meant to happen every day, or more constantly than my DD experiences it, as sometimes she is fine. But so many of the symptoms ring true with her that I can't help feeling that she must have it, though perhaps not as chronically as other babies.
I don't know if any of that helps, but I do know what you're going through and I sympathise. If it's of any comfort, crying is meant to peak at 6 weeks and get gradually better thereafter...