How do you point a subdomain to DigitalOcean without using or the original domain or changing nameservers?

I am using namecheap as my domain registrar for a domain, say example.com. Because of the way I have things set up and example.com pointing somewhere else, I cannot change the nameservers or use example.com and therefore want to use a subdomain, say ocean.example.com, to point to a Ubuntu 16.04 droplet with an example IP of 1.2.3.4

Based on what I have been reading, I believe it is possible to point to subdomains without changing the nameservers of example.com on namecheap, but whatever I try does not seem to work.

My questions are:

• What exactly do I need to do to the DNS settings on namecheap?
• Is example.com OR is ocean.example.com my domain that I create under DigitalOcean?
• What exactly do I need to do for the DNS configuration on DigitalOcean?

Thank you all for any help!!! :)