J.M.
This is not at all unusual for a one year old. Maybe you can try to using a baby carrier (backpack kind) in the house. You can cook, clean and vacuum. Babies have a natural instinct to be close to their parents - you can nurture that or try to thwart it. My experience was that when you nurture that instinct the kids grow up to be extremely self confident and independent. I know it sounds like the opposite would happen, but when you show them that they are important to you, and then they will feel important.
My daughter was always clingy. She wanted me to be with her or near by. She could be very brave if I was with her. If she was sick or teething she wanted to be held constantly. This is pretty normal behavior. I recommend these books:
‘The Attachment Parenting Book’ by William Sears M.D.
‘The Successful Child Book’ by William Sears M.D. (askdrsears.com)
‘The Confident Child’ by Terri Apter
My daughter did have a hard time adjusting at the start of kindergarten. (Since I did not send her to preschool this was the first time she was away from me for such a long time.)
However, she is now at the end of first grade and she had a great year. She is confident and resilient. She is a leader among her peers.