In my experience, pest control is related to vermin on common property and is arranged by and paid by the owners corp. If a landlord or tenant want their property specifically treated in addition to the common property, then the landlord or tenant would pay for that.
Does your lease mention pest control treatment?
If yes, then the question is why you agreed to such a clause.
If not, then regardless of whether you are asked to pay for the treatment, I believe you can reject doing so based on health grounds.
I suggest you (a) assume the landlord has offered to pay for the treatment (if there is no mention that you are to pay) and (b) write to your landlord along the following lines: “Thank you for the offer to treat the premises, but on doctor’s advice my state of health prevents me agreeing to treatment at this time. If my health improves and if my doctor believes that the chemicals will not affect me, at that time I will let you know”.
Ensure you have such a note from your GP dated before writing to the landlord.