Yeah, davinci-003 is gonna be gpt3, which is more expensive than 3.5.
One more anecdote: I've been running a half dozen gpt3.5 IRC bots for a few weeks and their total cost was less than a dollar. A few hours of playing around with LangChain on gpt3 cost me almost $4 before I realized I needed to switch to 3.5, though even then it still uses a ton of tokens every chain.