Congratulations on DS2! Crikey the early days of little babies is HARD WORK so you have my enormous sympathies.
DS2 was very 'hard work' and it is only now at 10.5 months that he has blossomed into a happy, content child! I am not writing this to alarm you but to make you aware that, personally, I don't buy the 'colic' tag. A really believe that an unsettled baby is unsettled because there is something upsetting them. However, in my experience, GPs are very unsympathetic and unsupportive.
The most obvious reasons that a baby may be unsettled are: dry/wet nappy, correct temperature, well fed and well rested. If those are being addressed (you mention that he is not sleeping/napping well) then please bear in mind the symptoms of silent reflux.
DS1 was diagnosed at 4 months after 4 months of hellish 'colic' behaviour. DS2 was diagnosed at 3 weeks and his meds are finally established (in terms of the correct medicines and correct dosage), hence why he is blossoming.
Signs of 'silent reflux' are:
*Back arching while feeding
*Only able to consume a 1-2 ounces at a time.
*screaming
*needing to suck (both DC had to suck heavily on a dummy between sucks on the bottle)
*unsettled
*terrible wind (really difficult to wind)
Tips that helped DC to settle:
DS2 would only settle on his tummy (I bought an Angelcare breathing monitor for my own peace of mind)
Swaddling (although DS2 hated it!)
Dummy
Heavy bum patting to get to sleep!
Cot/moses basket on an angle (put book at one end or a pillow under the mattress)
I would say that at 6 weeks, a baby needs to sleep every 1.5-2 hours during the day. Perhaps you could get a rocker/swing and when you have fed him put him in a calm place in the room (i.e. not too much stimulation) and let him settle to sleep? Hopefully the rocking will calm him, keep him upright (important in reflux) and enable him to drift off.
Anyway, a few ideas and I hope some other suggestions come along soon xx