Sometimes the -er(-or)/-ee juxtaposition conveys the relationships you are after, like in payer/payee, employer/employee, tutor/tutee, advisor/advisee,
At variance with this usage placing the -ee people at the receiving side, some sources indicate that a consultee is the person giving consultancy, that is the consultant, or in restricted sense, the consultor. So you find out a kind of harsh spot.
The consultee does receive questions thus. Then, beside the other suggestions given here, I would give a chance to inquirer or enquirer as per
https://www.thefreedictionary.com/inquirer. This sounds less informal than asker.
As a note, do not trust to spellcheckers to test the existence of a word, since they are often based on abridged dictionaries. Dictionaries are not the same, also; for example this one does not have any key for consultee, unlike the other two cited in this answer.
Disclaimer: not a mother tongue.
Please comment/edit after downvoting so I can learn from it.