J.C.
Two of my three children were thumb suckers and self soothers. They both weaned from the habit by the time they were 6 years old and permanent teeth erupted. I was told by two different dentists that breaking the thumb sucking habit before permanent teeth came in was in the child's best interest. So we did not worry too much about it until each child turned 5 years old.
When the thumb sucking became annoying or was clearly done out of boredom, we made sure to keep the child busy. My daughter's fine motor skills improved dramatically when she practiced cutting shapes or coupons (with child safe scissors). She is 13 years old now, and loves to knit, crochet, draw, and does beautiful origami folding.
My son would play a lot with clay and/or Play-Doh to keep his hands busy. He did not care much to draw or write. He was more tactile and liked things like playing in the sand and water. He still takes really long baths. He is 7 years old and enjoys building and creating things.
I would find age-appropriate toys and other manipulatives to keep you son busy, esp. when he is bored. I would not try to restrict the self-soothing when he is tired or sick, but offer reasonable alternatives.