My dd is 6 weeks and she did similar around 4 weeks. She now naps in the morning and afternoon but is wide awake for the rest of the day, she sleeps about 10/11-6 now (with feeds but settles quickly) so you may be on track for longer nights
I have the same problem with my 6 wk old. Only sleeps 9 to 11 hours in 24. Most annoying and very draining...sorry no advice to give. Just trying to get through as best I can with help from hubby and family.