I'm still within my first month at a new job. I have been under medical treatment for a while (months, years) now which require periodic appointments (e.g. orthodontic adjustments every 6 weeks, injections for a chronic condition once a month, doctor's checkups every few months. In general I am able to perform my duties as expected. As far as I can ascertain, I would not qualify under a disabled category that out local labor law provides protection for. I have been upfront about these health challenges from the interview stage, and the employer obviously has still seen his way open to offer me employment. To their credit, they are very accommodating towards all employees with flexible office hours and allowing some work from home where practicable (no telecommuting though).
I have recently developed another small but embarrassing and interfering medical problem - inflamed and bleeding hemorrhoids. I'm mentioning this explicitly to explain the excruciating pain while sitting at my desk or commuting, and fear of embarrassment through stained clothing. So I see it as a fairly serious impairment to my work (even though the problem itself is mostly easily treated). This made me leave the office to seek medical attention on short notice.
Currently, treatment includes using a shower or hand shower after toilet use, and lying down on my side in private to apply medication - and the office environment does not have facilities to make this possible there.
I should probably also mention that the new job is a commute from my home (and support network of medical practitioners that I know and trust) that is on the longish side. Leaving the office for a quick appointment may be a 2 hours gap if the appointments happens close to its time and is concluded speedily.
So on the one hand there are valid medical challenges to the normal expectation of providing labor. On the other hand I do not want to create the impression that I am trying to shirk responsibilities by making up all sorts of reasons, even before I have been able to prove my worth to the new employer - despite what the law stipulates, there is always the human factor.
How much explanation would be sufficient, and how much would be over-sharing?
Some people may be interested in the locale, but the company is a very diverse group with many ethnicities, religions and cultural backgrounds represented. I do know that the above problem is almost unknown amongst certain ethnic groups (and may thus not be seen as such a big issue), and I am also ignorant how various cultural backgrounds would look upon the discussion of such a private matter.