Sorry that's not spidy sense. Everyone does that. Now when you can shoot a web out your butt call me...that's evolution.
Is spider sense possible? Because whenever something gets close to me or something goes behind me I get a strange tingly feeling at the back of my neck. Have you had this? Maybe be a new sense developing? Maybe a next step in our evolution?
Could be that the fine hairs on your neck are reacting, sensing things in your energy field.
Happens to me a lot.
You are "Hyper Aware" of your surroundings.
Some people can sense patterns to the normalcy of their surroundings. Those things that fall out of place can set your senses on a type of alert.
Change in air temperature can be felt by the skin and fine hairs.
Change in air pressure can be felt both in the ears (inner) and also on the skin.
Sound - in the ears
Smell - nose
And peripheral vision works both on the sides, and the eyes can sense even the slightest alterations in light (Shadows).
Play all of these in unison to someone hyper-aware and you might as well have that sixth sense of Spiderman. You can train yourself to learn your environment and have those things that are different "Stand Out" to you.
If you have a small dog, you will notice they are Hyper-aware and they have senses that are several times more powerful . . Hence the seemingly barking for no reason.