You can get nipples made for rice in the bottles. Dr. Brown's brand has them. That being said, I think it's pretty early to be giving rice. The digestive system is so new. I had a 10 lb. baby boy that left the hospital eating 4 oz. bottles. He soon graduated to 6, then 8 oz. He ate like clockwork, every 3 hours.
Trust me I know how exhausting it is and I feel for you, but at just 23 days old, it's normal for a baby to eat every 2 hours for a few days. It's healthy for them to do so. If he doesn't start to stretch out his feedings soon, you may consider the possibility that he's not really hungry. All of my children have had acid reflux and it makes them cry. They would take a bottle because it temporarily soothed them. You can also try to stretch out feedings yourself by putting him off for 15-30 minutes by soothing him other ways, like with a pacifier. He might figure out that it's ok to go longer between feedings. Gradually stretch him out to 3 hours.
BUT PLEASE consult your pediatrician. He/She will be able to tell you what is normal and what's appropriate for his size, growth rate and age.
Wishing you rest : ) OH, AND YOU HAVE TO TRY THE MIRACLE BLANKET FOR BETTER SLEEP! www.miracleblanket.com