Yes a toothache will eventually go away on it's own.
Most toothaches have pain that comes and goes and the toothache pain will usually go away within the same day or within a few days or so.
If the toothache pain does not go away within a few days or gets worse or comes back to often then you should make an appointment with a dentist and have the toothache checked out.
If the toothache is caused by a more serious infection of the tooth then it can spread and then the tooth infection could cause gum disease as well as lead to poisoning of the blood.
In rare cases a toothache that is severe enough can lead to death if not treated.
If you have tooth pain or a toothache it's best to have the toothache checked out just to be sure it's not serious.
You can use a warm tea bag to help ease toothaches, use some orajel or other tooth numbing product and gargle with apple cider vinegar.