Is it normal to want to be alone??

yes this is normal. Sometimes I feel the same way.

Yeah, solitude has its enticements.

It's a long battle, and yet, in the end, there's only you, even if you're not alone at the time.

Sucks, but you've got to weather it to get through it.

...

Oh yeah, did I forget to mention that there is a 'through' it?

: ]

yes, it's normal, nothing wrong with that.

The way you've described it, it doesn't like the ideal situation. It sounds like perhaps you've had bad social experiences or feel you've been repeatedly hurt by family/friends.
I'm just guessing here, but, if that's the case, it may have instilled a deep cynicism and lack of trust towards human relationships/interactions and a fear of ulterior motives.
If that's the case, that's very unhealthy. We're social animals, most of us don't fair well when we're truly alone.
However, if being alone is a way for you to reflective on yourself and life and work things out, then that's a positive activity.