Immortality - Gift or Curse?

Now since I don't have much to go on I will assume the following things:

You cannot lose arteries while 'immortal'
You cannot be killed by any means while 'immortal' ( Starvation, Lack of oxygen, etc. )
You can/can not feel and are/aren't able to be stopped pain while 'immortal'
Your 'immortality' can not be transferred to anyone in any way
You can not get infected by any diseases

In this example, we will assume your age as being 25.

So let's say you are immortal, not going into how or why or when it happened.
Well at first it might be a bit weird, you do not fully understand this new trait of yours,
not many people would notice and people would probably not believe you if you told them.
After maybe a couple weeks it has become normal, you may have made some people believe you by this time, and maybe have won some bets.
You still don't know what your limits are but you aren't willing to risk dying to find out.
You aren't getting sick in winter as you normally do even though you are outside all the time.
One day you accidentally fall off a cliff (logic) but are surprised when you are not injured in any way, and after this,
you realize that you may be more invulnerable as you had first thought and you are not as careful in yourday to day life.
You try to make public demonstrations about how you are somewhat 'immortal' however nobody believes you and just thinks it is an elaborate trick.
As your attempts to become famous for your 'immortality' fail you start to care less and are tired of your job, and get tired of taking orders from people.
You start to rob stores with nothing but a kitchen knife, without having to fear retaliation, the police try to take you out but their attempts fail and you always escape.
At this point you are wanted by the state, you have gotten the fame you wanted but are hated by all, immortal in life and immortal in the nightmares of the families you have destroyed.
You have at this point stolen weapons from random police officers on the street who can do nothing but helplessly watch as their life ends.
The only thing you see on the streets is police car after police car on the search for you.
You get tired of living here and you find a way to another state, in which you are nothing but a rumor.
However, they soon realize that you are far more than a rumor. Everywhere you go you cause chaos, and every law enforcement officer in the country knows your face.
You are searched for everywhere and the main priority of all major crime fighting organizationsand lynch mobs roam streets as they see the government isn't stopping you.
At this point the amount of people against you is overwhelming and you fear that if any of the mobs of people catches you there will be too many to kill and they will simply overpower you.
You fear being locked in a cell for the rest forever so you take to the shadows.
Picking off people under the cover of darkness, trying thin out the numbers, but it's no use.
You remain to do this for many years as it is too late to flee to another country, and so ends your story.

Now to answer the question,
Gift or Curse, well I think it would be more of a curse than anything.
If you do give yourself up for the good of humanity you will just be used against your will forced into slavery for the good of humanity, forever.
There might as well be no way to keep this hidden, as the years go by people will notice how you do not age and such.
You will simply be doomed to watch your loved ones die of age one after the other and you can do nothing to save them.
In the end it would always be shitty for you, but you can decide if you make it shitty for others.