You can keep up - this constant suckling is your DS telling your body how much milk to produce. Almost all babies seem so hungry at first, I remember being glued to the sofa for the first few weeks. The only time he wasn't being fed was when he was asleep.
Get some Lansinoh now (it's pricey, but it really is the only nipple cream worth having). You don't need to wash it off before you feed. Slather it on as much as you can and let DS suck as much as he needs to.
The best thing you can do, IMO, is to get somewhere comfortable, with lots of cushions, and just wear your pyjama bottoms and a comfy feeding bra. Get people to bring you cake, pots of tea and pints of water. Make sure the remote is close to hand, and have a box set at the ready (or Wimbledon, of course!)
Very soon this stage will be a hazy memory, I promise. We're still going now after lots of problems at the beginning, and DS is 8 months old. Breastfeeding is so easy now and, in those early days, I never ever dreamt we'd get to this stage.
Best of luck and congratulations.