You can replace your hard drive. Bad sectors are not objects that you can physically remove and replace. Windows has tools (Chkdsk, for example) that can locate these bad sectors, mark them as bad, and have the drive actually avoid using them in the future.
A failing hard drive, after only a year and half is bad... but not outside the realm of possibility. Typically, most hard drives (laptop or desktop) are good for 2 to 4 years... Western Digital and Seagate making better drives that usually last 3 to 5 years... either way, this is not written in stone. Many unforeseeable factors can cause drive failure.
So, what can you do? If you wish to save the data on your drive AS IT IS, you can use the Windows backup software to back it all up to DVDs or an external hard drive. You can also purchase a new hard drive (of the same size), a cheap portable external hard drive enclosure, and use free drive cloning software like Clonezilla to clone your existing drive onto the new replacement. You would need the cheap portable enclosure to be able to connect both drives to the same computer, at the same time.
Or, you could support your local community, and pay a professional at a local computer shop to do this for you.