It is dead instantly from air (so in your case being "airtight" will kill it instantly), but if it had some hiv in blood you might get infected if you shared it quickly with someone - that didn't happen so you should stop worrying.
You purchased a packaged new needle. That is different than a health care setting using used needles one after the other on people. There is no reason to believe that the packaged, new needle you bought was actually a used one. Your anxiety is running away with you here.
I'm sure you know the meaning of "instantly" so reread.
Could anybody answer my two questions?
1. I have purchased new syringe and used after 10 days to inject medicine. if it recycled or used, virus
stays viable for air tight condition. as there is no air. could it be infectious after 10 days also?
2. what time temperature will take to kill virus in syringe? Will it take more than 10 days ?