Yes, Google Scholar is a good tool for this task. But as I know, H-index according to Scopus and WoS is different from Google Scholar. Google Scholar's H-index tends to be higher.
Google Scholar can automatically calculate your h-index, you just need to set up a profile first. By default, Google Scholar profiles are public - allowing others to find you and see your publications and h-index. However, if you don't want to have such a public web presence, you can un-tick the "make my profile public" box on the final page of setting up your profile.