On a narrow screen there is no sidebar, no second column, and no room for six navigation items. You have to decide what comes first and what can be reached in one tap, and those decisions improve the desktop version too. Sites designed the other way around tend to arrive on a phone as a stack of elements in an order nobody chose, with the important thing somewhere below three things that were in the sidebar.
Whether your site uses it is not something you can determine by looking, since most templates are responsive either way. What you can check is behaviour. Load your site on a phone and see what occupies the first screen before any scrolling. If it is a large image and a menu icon, and what you actually do is somewhere further down, the design assumed a desktop. If the first thing visible tells somebody what you do and how to act, the priority was decided for the small screen.
Two other observable signs. Whether tap targets are comfortably sized and spaced, since a design scaled down from desktop produces links too close together. And whether the phone version hides content that the desktop shows, which was a common shortcut and means mobile visitors receive a lesser version of your site while being the majority.
If yours was built desktop first and works acceptably, this is not a reason to rebuild. It is a reason to check the specific things above and fix them individually, which is a smaller job than a redesign and captures most of the benefit.
There is a related habit worth adopting regardless of how your site was built, which is to write and review your copy on a phone. Text that reads well as a paragraph on a wide screen frequently becomes a wall on a narrow one, and the sentence that looked concise now occupies four lines. Reviewing in the format most people will read it in tends to shorten everything, which improves the desktop version as a side effect. The same applies to forms, which are where narrow screens punish a desktop assumption hardest: every field you can remove is a measurable improvement in how many people finish.