3 week old wont sleep?

My 3 week old just wont sleep... doctor said she has colic.. she goes through the whole crying in pain thing for hours but she gets to a point where we know she is not in pain.. she is happy she just wont sleep.. she stays awake for up to 16 hours!! we try everything, baths, feeds, cuddles, rocking in her bouncer, walking with her, all different positions, not holding her, having her in the dark, everything we can think of. Last night i let her cry for about 30 mins (giving her the dummy if she worked herself up too much) and that seemed to tire her out a bit she went to sleep after 8 hours last night (not of crying, it was about 20 mins after her crying) but so often she is up for at least 12 hours.. she is so tired but just keeps fighting being awake.. she sometimes falls asleep but as soon as we put her down she is wide awake and we start all over.. we are just so tired now and surely it is not healthy for her to be awake so long.. she is feeding great.. we been given infacol and that seems to be great for her colic and she is giving great burps and does not seem like she is in the pain she was last week... she is no longer comfort feeding either.. we have had some success but we need her to get some sleep... has anyone else had this problem?? if so what worked for you?? does anyone recommend letting her cry at this age?? yes im a first time mum don't know what we should and should not do.