Yes, a dedicated macro lens may be out of your budget - even a second hand one. The good news is that if you are new to close-up and wants to see what are the possibilities of creating interesting images in this genre, there are at least 2 lower cost options.
1. Close up lens.
When I wanted to experiment with close-up but did not have a budget for it, I bought close-up filters (sometimes called macro filters) instead. They are relatively cheap and the camera retains the auto-exposure and auto focus. Of course, with the filter on, the lens will not focus to infinity. You can build up a collection of these filters and stack them up to increase the magnification. The downside is (other than not able to do infinity focus) is that the image quality will suffer a bit, especially on the edges. The other disadvantage is that it has a fixed filter diameter you you need a step down/up filter ring if you want to use this on other lenses which have a different lens diameter. I don't think that these negatives should stop you from considering this option.
2. Extension tubes
Extension tubes is an alternative to the filters and they can be used on all lenses. They usually comes in a set so you can select the magnification range by using them individually or stacking them. I have used bellows before (something like extension tubes) and the magnification you can get is quite large - bigger than 1:1. However, my setup does disconnect the data connection between the lens from the camera so I need to switch to full manual. I think there are extension tubes which preserve the connection and I would strongly advise that you so look for these.
Below is a short video that gives a short clip on these options. Not the best but it will give you a visual idea.
