I think you may have to ask yourself why your mum thinks the ocd comes on when it suits you. Is its because you have ocd all the time, but at some points you can cope with it more than other times? So for her as an outsider, shes only seeing you having ocd sometimes, and not all the time?
I think your mum and dad will give you a bit more credit if you go to the doctor and ask for help. By doing this you and not your parents are taking control of the situation and they can see you wanting to do something about it. Then go and have that talk. Tell them that you feel the ocd on this that and the other occasion, and theres times where you have a coping mechanism, and times when you try that and it does not work and your not putting it on, it escalates and leads into a panic/anxiety.
My daughter, she had anxiety issues. She does not like new situations, or current situtions that have panicked her in the past rear its ugly head and make her panic again. For us as parents it is worrying, its also frustrating as well because you dont know what to do. She did go to the doctors who did know what to do and they gave her the help she needed and a year later is in a much better position than she was.
So please have a word with a doctor, and also if they refer to a group be it in person or online, take it. The more you talk about it, the more you feel able to have some sort of control over it, instead of suffering in silence.