I agree with other posters here with regard to "You adapt to your baby's schedule rather than trying to get the baby to fit around yours".
I was in this situation for 14 months. Surrounded by people who's children napped in the day AND slept through the night. Was there a correlation between the fact I was the only mother Breastfeeding? Who knows? But what I can say is that yes, I was exhausted and if it wasn't for Mumsnet I wouldn't have known as I didn't have that support and knowledge around me.
It is really tough and exhausting, most days I would threaten to move on to formula as I was convinced it would make a difference.
I didn't for personal reasons and decided that for me, it was worth persevering and that i would be more upset if switching didn't make a difference and I lost the opportunity to feed in the way I had chosen.
Up until 14 months my baby slept 2 x 20min naps through the day and woke every 2 / 3 hours on average over night. I also went back to work fulltime at 9 months so it was a struggle to say the least.
I must stress I put this on myself and there is no medal for doing so. I honestly thought I would never have a 5 hour sleep stretch ever again (the thought of 8 hours was too far fetched and beyond unrealistic).
What changed at 14 months was her time spent walking increased and I stopped breastfeeding. Again, cannot confirm correlation.
Since then from 14 - 18 months she slept though 12 hours a night with a 1 hour nap in the afternoon. From 18months - onwards she gave up on the 1 hour nap but still sleeps for 12 hours a night.
What I am trying to say is I have been there, it's not nice and it might not improve anytime soon but please know there are many of us who have been there and we will continue to be there for you if you need us.
I think honesty is key here and hearing that your situation is somewhat normal can only be a comfort in a time of great stress and change.