Some less severe sinus infections do go away on their own within a few weeks without treatment or antibiotics.
However if the sinus infection lasts longer than a few weeks then you might have a more severe sinus infection and need to see a doctor or go to urgent care and get treatment and antibiotics.
For at home treatment for sinus infections you should use a neti pot, take a steamy hot shower, use a humidifier, drink plenty of water and get plenty of rest.
Also taking some sinus medication you can get over the counter can help somewhat but if the sinus infection doesn't go away within a few weeks I would advise seeing a doctor for treatment.