If you get another drive and put in your computer, get a HGST Data Center quality drive. The HGST seem to have lower failure rates than the more common drives people buy and the Data Center quality drives are a little more heavy duty.
Keep in mind that writing the data to a drive in the same computer eliminates some of the benefits of a backup. If someone steals the computer, your backup is gone, too. If there is a fire or flood, it's gone. If you take your computer in to have it worked on and the technician accidentally erases the drive, it's gone.
As for external drives, we've had far more failures here with external drives than internal drives in spite of having far more internal drives. For example, the only external drive I've personally used quit after a year or so. Also, one of my oldest brothers had two external drives fail within weeks of each other about two months after he bought them and lost everything on them.
External drives typically have shorter warranty periods for good reason.
It really boils down to how important your data is to you.