My DD wet rivers for the first few weeks, then settled down a bit.
I definitely agree that boosters would help. Re. night nappies, Weenotions Night Notions are good, and so are Upsy Daisy night nappies - I'm not sure if either is available in size small though.
The first few weeks of motherhood are harder than anyone tells you, and the sleep deprivation doesn't help. It will get easier, I promise