Oh hun, MadB is right - it's completely normal! My boy is about the same age (5 weeks tomorrow!) and tends to want to be a stickybeak and fight sleep. I find the "feed-play-sleep" routine all the books say to use is no good for us, he tends to prefer a little top-up feed and to be cuddled to sleep before I can put him down. I think it just helps him relax and wind down a bit more so it's easier for him to drop off.

When it comes to getting out and about, I'd suggest look into a carrier or sling - Penguin loves his (I have an Ergo) and will quite happily snooze his way through an entire shopping trip, or occasionally wake up and "talk" to me as we go about our day.