NO you are NOT Schizophrenic and WONT develop it...
This is a classic obsessive DP fear....It is a form of PURE OCD....
Every DP sufferers biggest fear is they will lose their minds at some stage or that what they are going through is something much more sinister or the beginnings of it...
Trust me if you were schizophrenic everybody around you would be very very aware of it...I bet if you ask the people around you do you appear odd or are you behaving odd they would say NO you look and appear very much normal to them...
In fact if you were schizophrenic you probably wouldnt even be aware of it yourself....
You are experiencing classic obsessive fearful DP thinking patterns...In time you will recognise it for the crap it is and it will stop frightening you...Thats when it vanishes...