I don't think this is a matter of your hair being soft (and I honestly don't think most black (African American, whatever) people don't have soft hair. I think the word you are looking for is fine
By the way your description sounds like you have fine hair, not necessarily softer. When you have fine hair and you do too much moisture or too many braids, or too much blowdrying it is going to get spongey or stretch and snap/ break like what you are saying it is doing. By the way, if you are in Arizona it is dry out, you may want to consider stopping the shampoo and addnig a conditioner that has protein to your regimen, maybe a regular rinse out conditioner wtih protein everyday could make a difference.
BTW I have fine and coarse combination hair. The fine hair I have has never survived any kind of heat tool or braids the same way my coarse, thicker hair has. It will get mushy and snap off so I have had to stop using heat to let it grow out. Protein conditioners help, not the strong treatments, but a daily use of some kind of light protein overtime has helped.
APL, coarse, wirey, curly, coily, wavy, kinky
I'm just trying to maintain...