I had similar problems when I first started getting symptoms. I was still in school then, but I wasn't diagnosed until a lot later. It was hard not having a diagnosis. I was told I had Irritable Bowel Syndrome which meant I didn't even have the claim that I had a "real" disease - Irritable Bowel Syndrome isn't treated as a legitimate cause for problems and isn't viewed as being anywhere near as severe as Crohn's.
I was terrified of having diarrhoea in public and having to leave lessons to use the horrible school toilets where you could hear everything through the cubicle walls. My intestines would make these horrible gurgling noises (not like the normal rumbles of hunger) when I was in a quiet classroom.
I did come to accept my illness though - but it took a while. By the time I went to uni I had learned some tricks. I used my uni disability centre to make sure my lecturers would allow me to leave the room whenever I wanted to. (The disability centre just sent an email to my lecturers stating that I had to be able to leave for medical reasons - they didn't tell them my symptoms.) I got bathroom breaks during exams too. If I'd made similar arrangements when I was at school I would have found it much easier.
If concentration is an issue for you, you may be able to get extra time on assignments. You usually just need a doctor's letter to show to whoever deals with such issues at your school - maybe your tutor if that's the set up where you are.
My family didn't understand my embarrassment either. I tried so hard to keep the symptoms hidden that they didn't realise how bad they were! As my illness has progressed it's become impossible for people not to notice, and I do get more sympathy now but I guess having to get worse in order to acheive that was probably not worth it!
I still find this illness embarrassing, but now if I do have something embarrassing happen, I don't dwell on it any more and I don't worry in advance.
It helped me to read online about others with similar issues. I saw that there were nice people, who had families that loved them and who were, for the most part, living active lives. I realised that I wouldn't care if one of these people had an embarrassing bowel incident, which made me realise that most people wouldn't care if I had one either.
Finding incontinence pads existed helped me enormously - I'm not sure if that's an issue for you.
And of course getting a diagnosis - or at least when I reached the point where doctors were realising there was actually something wrong with me other than stress - did make a difference, even though it shouldn't. It gave me permission to have problems. Rather than feeling I was responsible for my embarrassing symptoms because I couldn't manage stress well, I learned that it was caused by a medical problem and didn't reflect on my character - which of course should be true even for people with Irritable Bowel Syndrome, though doctors don't seem to treat it that way.
I think you will be able to come to terms with this as you get settled back in school. Do you have friends who know? Your family may well learn more with time too. Maybe showing them posts by others on this forum or asking them to learn more about your illness would be helpful? Just remember your family's perception of your illness is not necessarily accurate, and try to give yourself permission to be ill and, yes, to be embarrassed at times - it's a normal, natural reaction, one we all go through. The thing is to keep it in perspective.