Should I quit my job or not

I just moved to Japan around the end of July and started my new Job here on August 1. We had a 1 week of training (mainly discussion) and then they flew me back to my home country to accompany my team members there. I went back to Japan a week after and around Tuesday this week, I got a fever. Thursday came and I still haven't recovered so I did an covid test and tested positive. I scheduled an online check up the same day and was asked to rest at home until I'm fully recovered.

The thing is, I was asked to go to another country for some exhibit. The flight was supposed to be on Sunday. I shared what the doctor told me to my team leader and ask if it's possible not to go which they said they will consult with our section manager. Moments later, he told me he will go in my stead so I can rest assured. Then today, I got bombarded by messages that I should just move the flight to the 25th (cuz "there is no flight available left on the 26th"). I have not fully recovered yet and is still in pain but they forwarded with the plan as if I already agreed to it and they're asking me to reschedule it myself since I have the account.

The overall work schedule of this company is quite harsh and it's taking a toll on me both physically and mentally. I'm actively looking for jobs but I'm not sure if I should just quit now or wait for a new opportunity. I'm not even sure if I can secure a time for job interviews due to the tough schedule.
I need some advice.

Edit:
So my manager told was the one who announce that it was me who wanted to have the flight me (albeit me not saying any of that sort).

by Specialist-Aspect-35