As i was out of the city for like two months i couldnt purchase my Apple care, and it has exceeded. Is there a possibility for me to buy a new one yet?

I bought my mac last year August and it was working really well like thrity minutes ago. I was out of the city and in Sri Lanka we have a very less number of serice sations which is only in Colombo. I was out of the city and i coulnt buy the apple care due to the unavialbility. Is there a way that i can buy one now ? i am getting a thin whitish /bluish colour line in the middle of the screen. It was not there like at all and my computer works really well as well. What can i do? Can i buy an apple care? anyone have an idea what has gone wrong?

Please help me..