How can I get a list of citations for a DoI or PubMed ID?
Quick and dirty version: Google Scholar

Type-in the DOI and read the citation count on the field "Cited by". Google Scholar does not filter for quality, so the citation count will include self-published papers, fake publications, etc. Expect some noise.

Better version: Web of Science

Ask your institution's librarian how you can access the Web of Science database and how to use it to retrieve the data that you need. That might require you to walk in daylight to the physical location of your library. Many survived that journey.