There are some really simple ways to check whether Google accepts that your website is mobile-friendly;
1. Search your own website on your smartphone. If you have a “mobile-friendly” tag next to the result then Google has registered your site as mobile-friendly. This is how the tag looks;
2. Click this link and Use this Google mobile-friendly test . Just type in your website URL. Google will give you a yes no answer with a mobile usability report explaining any issues.
If your website fails the test you have two options (I don’t think doing nothing is an option):
a. Change your site to be device sensitive addressing issues identified in the test. That is, the website automatically presents mobile format or web format according to which device (mobile/desktop/laptop) the consumer is using to search. This Google “Get started” page will help.
b. Develop a new mobile version of your site.
Unless you are competent in web development, I strongly suggest you use a web designer for these options. It is possible that you could do the site re-design option yourself using DIY platforms, but it is not something I would recommend.