5 year old bed wetting

Does anyone have any tips for how to deal with nightly bed wetting? My 5 year old son wets the bed every single night. We cut off fluids and make him use the bathroom before bed. Which I was told by his pediatrician does not even matter. She said it's completely normal and he will grow out of it. I understand its not his fault but it's very frustrating. Especially when I'm up all night dealing with a new born and can pretty much expect my son to come wake me in the few moments of sleep I do have. At this point he isn't even able to sleep with a pillow because every night the pillows get drenched with pee. It's starting to really wear on me. I'm tired of cleaning up pee sheets and clothes every day. At this point we can't afford to do laundry every single day. We also can't afford to keep buying pull ups right now to keep him dry. So basically I end up changing him into a fresh sheet and blanket every single day and take the clothes and blankets and sheets to hang outside to dry until laundry day. Does anyone have any tips with dealing with this? My sons pediatrician said it could last even all the easy till he's 10. I can't see myself going through this every single day and night. Please any suggestions as far as keeping things dry will help. I know him not peeing is not in his control so it won't likely stop till his body is ready