He cannot shave his head or cut his hair during ‘umrah because his head is very sensitive; what should he do?
Question

My head is very sensitive and I have shaved my hair off completely. I am going to do ‘umrah in sha Allah; what should I do about shaving my head? Please note that I cannot shave my head and I cannot cut my hair. If I shave my head, the sensitivity will come back.
Praise be to Allah.Shaving the head or cutting the hair is one of the obligatory parts of ‘umrah for men; a man cannot exit ihram unless he does it. If a person omits one of the obligatory parts of ‘umrah, he must do it if there is still enough time and he is able to do it. If he is not able to do it or he misses the time for it, then if he had an excuse there is no sin on him, and he has to offer the fidyah. If he did not have any excuse, then he has sinned and he has to repent and offer the fidyah. The fidyah is a sheep that is fit to be offered as an udhiyah (sacrifice), or one seventh of a camel or one seventh of a cow, which is to be slaughtered in Makkah and the meat distributed to the poor of the Haram; he should not eat any of it. 
The scholars of the Standing Committee said:
If a person omits any of the obligatory parts of Hajj or ‘Umrah, he must offer a sacrifice. The sacrifice may be one seventh of a camel, one seventh of a cow or a sheep that is fit to be offered as an udhiyah (sacrifice). It is to be slaughtered in Makkah and the meat distributed to the poor of the Haram.
End quote from Fataawa al-Lajnah (11/342). 
Shaykh Ibn ‘Uthaymeen was asked about a man who exited ihram for ‘umrah after circumambulating the Ka‘bah (tawaaf) and going between as-Safa and al-Marwah (sa‘i), and he did not shave his head or cut his hair, then he entered ihram for Hajj. What does he have to do? 
He replied: 
What appears to be the case is that his tamattu‘ Hajj is not invalidated and is still valid, but he has to offer a fidyah (ransom) for failing to shave his head or cut his hair, based on the well-known view among the fuqaha’ that the one who omits an obligatory part of the rituals must offer a fidyah for that.
End quote from Liqa’ al-Baab al-Maftooh (5/4). This applies if he has some hair on his head that he can pass the razor over and shave it, as he mentioned in the question that he had shaved it. 
But if he went to ‘umrah having already shaved his head just prior to that, and there was nothing left on his head to be shaved, then he does not have to shave his head or offer a fidyah; rather when he finished his sa‘i his ihram ended, and he does not have to do anything further. 
See the answer to question no. 95439
For more information, see the answer to question no. 82077
And Allah knows best.