I don't really see any problems with your current routine so I am not sure why you are experiencing this damage.
But here are some suggestions:
Instead of pulling your hair into puff to air dry, it may be a good idea to band your hair in 8-10 sections. The more sections you use the less tension on the hair. Excessive pulling on the hair when it is wet can cause breakage.
Did you notice the splits before or after you used the Tangle Teezer? Some people have reported that they got split ends after using it a few times.
Do you do a pre wash treatment? If not you may want to consider doing one to protect your strands from absorbing too much water.
The following article written by Tonya McKay discusses the effect that washing can have on the hair: http://naturallycurly.com/curlreadin...hich-is-better
I have copied and pasted the relevant section of the article
"Normally, when hair is saturated with water during the washing process, it absorbs up to 30% or more of its weight in water. This causes each strand to swell considerably, which can lead to several undesirable effects. Increasing the diameter of the hair shaft causes the outer covering of cuticle scales to lift and separate, which increases tangling and breakage. But, perhaps more subtle, is the damage done over time from many cycles of expansion and contraction.Hair is a highly complex biomaterial composed of layers of differing materials, ranging from varying types of keratin structures to pigment molecules to fatty acids. When it is saturated with water and swells and then subsequently dries via natural or thermal means, it undergoes what is known as differential drying and differential deformation (because each separate type of molecule within the overall structure dries and deforms at differing rates). This leads to moisture-induced stress on the hair, which can lead to delamination (cuticle layer stripping off), breakage, fiber fatigue, and rupture (split ends). This whole phenomenon is referred to as hygral fatigue. So, anything that reduces hygral fatigue is great for the health of your hair in the long term."