It could be a spirit, or it could be paranoia. Spirits are all around us but most can't sense them. The feeling of being watched is how most people feel when a spirit is nearby. On the other hand, if you've finished watching a scary movie, or someone is picking on you, you could be worried and constantly looking over your shoulder. Subconsciously you would notice these things but your waking mind might not, causing you to conclude there's something following you.
Another option is a blocked root chakra. When the root chakra is opened you feel grounded and comfortable in your skin, when blocked you feel nervous and as though you are being watched.