I am naturally a bit hypersensitive to seasonal changes and environmental pollution. At times I develop sinusitis which is associated with headache ,nasal congestion, rise of temparature. Such condition prevails for 3 to 4 days from the onset. If nocturnal emmision occurs during that time is a ghusl (obligatory bath) necessary?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. 

A wet dream that causes ejaculation of the sperm obligates the bath. So, if you ejaculate sperm then, you must take a ritual bath as long as you are capable of using water. If you are not able to use water or using water can harm you or increase in your illness then, you may make Tayammum (dry ablution). However, if it is possible to wash some parts of body, then you wash them and make dry ablution for the remaining parts of the body. Know that the decision whether the use of water is harmful or not should be made only by a relievable medical doctor or by previous experience. Imam al-Nawawi said: 'If an impure person, who has to make wudu or Ghusl, finds water but fear that using of water could harm him due to severe cold or illness then he may make Tayammum as it is permissible for a sick person. However, if one can wash each part of the body and cover it before moving to other part, or can purchase hot water for a reasonable price, or hire some one to heat the water for reasonable wages, then one should do so. If one is able to use water, then making Tayammum is not permitted, neither for a traveler nor a resident. If one does so, his Tayammum is not correct; thus he has to repeat the prayer. Finally, if one can wash some parts of his body, then he should wash them and make Tayammum for the remaining parts' [al-Mujmaa']
Allah knows best.