Sorry to see that your question hasn't received an answer yet. Unfortunately, after this much time, it is unlikely that an answer for this specific question will be provided. For people still landing here via search, you can use htop to find out which program is using up the CPU- see https://www.digitalocean.com/community/tutorials/how-to-use-top-netstat-du-other-tools-to-monitor-server-resources#process

High CPU usage spikes do not incur any extra charges. Consider setting up a monitoring alert so you are notified whenever CPU usage is high: https://www.digitalocean.com/community/tutorials/how-to-set-up-alerts-with-digitalocean-monitoring