A swollen battery after a month would clearly be a covered defect under the limited warranty. As long as it doesn't show any signs of damage that aren't a result of the swollen battery, you should be able to get a replacement at an Apple Store regardless of where you got it as long as the first sale from an authorized dealer was within the warranty period.
Whether or not a suitable replacement is in stock is another matter. I've gone to Apple Stores where I needed a replacement device and they were never able to give me any real time availability unless they determined that my device was eligible either under warranty or if I was willing to pay the service replacement cost. For iPhones, they will only replace with the exact same model, color, storage capacity, and (I think) carrier if it was a carrier locked phone. And they usually don't replace them out of retail stock, but will need to have replacement devices. It wasn't an iPhone, but I had an iPad replaced recently and at an Apple Store they found a "white box" replacement unit was in stock at a nearby store where they were waiting for me. Not sure what you have (coolblue is in the Netherlands?) but it may be something that needs to be ordered.
And before going, it's probably a good idea to back up your iPhones's environment - preferably to a PC or Mac and then turn it off with the swollen battery. They may or may not give you an opportunity to transfer the contents at an Apple Store.