If you are over 18 years old, then it's still 5 days isolation recommended, which indeed brings you to Thursday. [The current guidance is 10 days before meeting people with weakened immunity systems]. I don't think there is a specific COVID guidance out, but there is a general policy allowing flights to be deferred until you are well enough to travel. If you are Gold then it's done on trust, below that you may need some paperwork / photo of the Lateral Flow test to assist with this. Consider wearing a face mask if you do go on Thursday.

Maybe on Tuesday, send an email to the BAH duty office, if you don't think you have improved enough? Otherwise keep hydrated and I hope you get over this.

https://www.nhs.uk/conditions/covid-19/covid-19-symptoms-and-what-to-do/

https://www.nhs.uk/conditions/covid-19/how-to-look-after-yourself-at-home-if-you-have-covid-19/