Henri, I have an HP all in one printer (inkjet) and I ended up buying a photo printer.....the prints you get on an all in one just don't compare to ones from a specific photo printer, IMO.
Try it, maybe you'll like them....a few sheets of paper won't matter just to try it. If you don't like them, you can continue to print at a store or buy a photo printer.
FYI, if you buy photo paper that is the same brand as your printer, you'll get better prints. If you skimp on the photo paper, you'll see a difference in the quality of your finished photos.....