Given that you have already had x-rays, this does most likely rule out a fracture of the bones in the finger. Nevertheless, sprains of the ligaments in the finger are very common, and since ligaments heal very slowly, swelling, stiffness, and pain can sometimes last for quite a while, often longer than one month.
Nevertheless, I would recommend going to see your primary care doctor
about this issue. They will be able to examine the injury
again, just to make sure that this is nothing more than a sprain. If it is a sprain, there are several additional strategies that they might suggest to you to help speed healing and limit pain. These could include taking regular doses of an anti inflammatory medication like ibuprofen. They also may recommend splinting of the finger, which helps to speed healing by immobilizing the ligaments and giving them time to heal.
In rare cases of very severe sprains, where for example the ligaments have actually been torn, it may be necessary to consult with an orthopedic surgeon
for consideration of a more invasive treatment of the problem. Your primary care doctor will be able to help you decide whether this consultation is necessary at this time.