A few months ago I started to take some of my images in Raw. I use Lightroom to post-process the images. At first I might keep a image in a certain folder, but after a while want to move the image in a another folder. If I do so, I lose any raw modifications I did. So what should I do in order to not to lose my changes?
The simplest approach is to simply not move files managed by Lightroom outside of Lightroom -- do it in Lightroom instead. In the Library module in the left sidebar, find the Folders section and drag the image within your computer as shown there. That'll keep Lightroom aware of where the file is and you'll always see it with the changes you've made.
It sounds like you have Lightroom set up to use a file separate from the original RAW file to store your edits, it is called an XMP Sidecar. When you move your RAW file you must also move the XMP file to retain your edits.
From Adobe: About metadata and XMP
File information is stored using the Extensible Metadata Platform (XMP) standard. XMP is built on XML. In the case of camera raw files that have a proprietary file format, XMP isn’t written into the original files. To avoid file corruption, XMP metadata is stored in a separate file called a sidecar file.
When using lightroom, you should not lose your changes when you move files. You simply have to update their location in the catalog. Upon moving the files, it should start listing the images as missing.
You should then be able to go to the Library tab, open the Library menu and choose "Find Missing Photos". It will then display the previews for all the photos that are missing. In the corner of each of the photos on the Grid view, there will be a little question mark. Click it and choose the new folder and Lightroom will reassociate to any files in that folder that it can identify.
I do this routinely when moving projects from my working drive to my archival drive.