It is difficult for me to tell from your description whether your fingernails and cuticles are infected, or just swollen. For this reason, you should probably see a physician about this problem. The types of physicians that would see you for this issue include primary care physicians and dermatologists
. An infected cuticle is called a paronychia. It is a small abscess found under the cuticle that can be quite painful. Treatments that some doctors
prescribe are antibiotics and/or surgical drainage. Another possibility is that you have a viral infection that can effect the finger tips known as a herpetic whitlow. This is caused by the herpes simplex virus. They can be caused by finger exposure to the saliva of someone with cold sores (herpes infection of lips) I suggest you schedule an appointment with your primary care physician
to better evaluate your cuticles. You may need some topical antibiotic ointment, or perhaps a short course of antibiotics if they seem infected. If they are infected and a small abscess is suspected, then they may need to be cut open and drained. Also, you can get some guidance as to why this is happening if measures you can take to prevent it from happening again.