It's been a long time since I went through puberty but I don't remember my facial hair tingling.
Does facial hair tingle on your body during puberty, and if it does does that mean your facial hair is growing for teenage boys?
Any type of tingling on your face is related to facial nerves firing across the face to make connections to other nerve endings.
I don't think hair growing would do that.
But if you have any amount of pimples or acne you've been treating or trying to heal on your face, that could possibly be casing that sensation.
But beard growing? No, very doubtful. (Don't worry, before you know it you'll be shaving and wish you didn't have to ;)