All Uganda medicals are done in Nairobi, Kenya at Gigiri IOM, unless there's another new Centre I don't know of
My advise would be that if you already have appointments and this opportunity is important to you then arrange all your diary plans to be in line with your appointments
But if at this point your job is still more important than the appointments then advising you will be a tough nut to crack
All the best in your choices
If I were you and there is no response on email or call and I have appointments, I would attend to the appointments