I have to say that ‘just’ adding wrappers is not going to make your site suddenly responsive.
In ‘most’ cases you have to think about where you want elements to be at different viewport sizes BASED on your current HTML structure & CSS.
In (with no empirical evidence) MOST cases, making a site responsive will involve a rebuild.
That’s not to say that you can’t re-use the existing code but sometimes a complete re-think / re-design is the only way to go.
Try to think…”How would I code this if I was starting at mobile size’ and then go from there.