Sorry to hear you are unwell. If you are in the court process it is important to comply with court deadlines. You could ask the other side to agree an adjournment. One of the reasons to adjourn may be that you are going to mediation.
An application to court can usually only be made after mediation has been offered and rejected or tried and failed. It is often used as a means to obtain full financial disclosure if it is not forthcoming on a voluntary basis.