I am not able to connect to internet in my EC2 Linux instance

How are you reaching your instance via putty? VPN or Direct Connect for example?

If you want the instance to be public then give it a public IP and ensure you have a default route in its subnet route table for 0.0.0.0/0 to the Internet Gateway (this makes it a public subnet). Have your instance's security group allow all outbound traffic. Have your subnet ACLs open as default.

If you want only outbound internet access then out it in a "NAT" subnet with a default route to a NAT Gateway that's in a public subnet.