Practically speaking the treatments that can be done at home do come with a certain degree of risk and no doctor in good conscious would ever tell anyone to mess miss an infected ingrown toenail themselves when seeing a professional is an option.
Having said that there are some simple home treatment options that are noninvasive and when done properly can serve to mitigate pain until a consultation with a professional can be arranged.
READ THIS WARNING:
Before attempting the tactic described below make sure that the toenail clipper nail file you're using to create space between the nail and skin is completely sterilized in hot or preferably boiling water.
Also to further reduce the chance of spreading an infection to an open sore around your ingrown toenail wash your hands thoroughly with soap and water before attempting this procedure and finally if these instructions are unclear or confusing don't start blindly attempting experiments on your foot and instead at the very least search out some more info before trying anything drastic.
When dealing with uninfected mild ingrown toenails that are caught early enough the most popular strategy for curing an ingrown toenail is to apply a pain relieving topical solution like Outgro to the bothersome area for a period of at least a few days so that the skin around the trouble area is numbed and the sensitivity is reduced. Once the spot where the toenail is growing awkwardly into the skin is brought under control from a pain perspective the pointed nail file from a pair of toenail clippers (pictures below) can be used to work out the offending protruding small piece of toenail that's causing all the damage.
Often times it's a matter of working the small pointed nail file completely around the corner of the nail from back to front (around the troublesome area) so as to create space between the nail and the skin. This should be very deep and does not need to be very painful. Slowly work it out and do not further injury yourself by prying to deeply or aggressively. It may be helpful at times to use your fingernails to help work space between the corner of your toenail and the surrounding skin.
When the offending tiny portion of the nail is finally removed it's incredible to realize how such a minuscule piece of nail can cause such terrible pain.
Being relieved of that pain by your own research and efforts is a tremendous feeling.