All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is impermissible to perform Tayammum (dry ablution) except if water is not available or one is unable to use it due to an illness or the like. The condition you mentioned is not a valid excuse by which it will be permissible for you to make Tayammum.
However, you should know that scholars held different views on whether one has to wipe the whole head (from ear to ear and from forehead to the back of his head) during ablution, or it is sufficient to wipe over only a part of the head. The Shaafi‘is and many other scholars held the latter view. As a layperson, you may follow this scholarly view if it would be make matters easier for you. We believe that if you follow this view, the problem will be solved.
Allaah Knows best.