This is completely normal for a 1 month old site. google is still figuring out what your site is about. this phase is called the google sandbox, new sites get unstable rankings for the first 3 to 6 months. keywords jumping up and down every day is google testing your pages against different search intents.
what helps speed this up
keep publishing content consistently. don't stop. build a few quality backlinks, even 5 to 10 real links from relevant sites tells google your site is worth trusting. make sure each page targets one clear keyword and matches what the searcher actually wants. avoid thin content, celebrity niche is very competitive, your pages need to be better than what's already ranking.
If your site is clean and content is solid, rankings usually stabilize around month 3 to 4. just don't make big changes to the site right now. let google finish assessing it.