h-index
What is it? Variations. Not necessarily the best measure for most early career researchers.
An h-index of 5 means 5 articles (items) cited at least 5 times
Google Scholar is easiest, but look at Web of Science's. I can look that up for you. (Also look at Scopus', if you can access). Here is Google Scholar's page about setting up a profile.
Alternative that might be useful -- Do it yourself analysis
Track one by one who is citing you. Google Scholar, Web of Science, and other sources. Scopus too, in PlumX (in APPsearch). (This is a task that a grad assistant could do, but I can do some for you also, if you're not in a hurry.)
Altmetrics
Altmetric donut, PlumX (APPsearch), and other services, but fairly easy to search among components (Facebook, Twitter, news, etc.) you care about most. One measure you will also see is downloads.
Examples: Donut in Wiley, Springer, Sage. PlumX in APPsearch and Science Direct. Also see Dimensions' and change Sort by -- Altmetric Attention Score.