Being on oxygen is never a good thing because it means you cannot breathe properly without the use of oxygen from a concentrator or oxygen bottle.
But when you're on oxygen it's pretty safe as long as you're trained to use the oxygen properly and don't get too little or too much oxygen.
However some people do experience some side effects such as bloody nose, dry nose, fatigue, morning drowsiness, headaches, irritation of the skin around the oxygen mask or from the hoses.
Some patients on oxygen also experience side effects such as nasal dryness or even mild ear pain.
If you experience those side effects while being on oxygen it would be best to speak with your doctor and let them know about it.
They may need to reduce your oxygen level or change the amount of oxygen you need.