My parents wont let it rest?

I was late developer and had my first ual experience whenI was 24 years old. Defining my uality throughout my life has not been easy. I have started dating this great girl and am very happy and confident with my uality now and consider myself straight - I have never been with a bloke and do nothave the desire to. The problem is, is that I have just got back from holiday and my brother and I didnt get on well and implied he thought I was gay which pissed me off he said that we all knew" I apprached my parents about this and they did not know why he said this. When back home when having an argument in front of mum and dad he said that I should come clean about my uality. Parents upset, I said I was not gay which I am not. Anyway my bro and I have sorted it out now but mum wont let it go - she asks why my bro thought that. I think my bro has seen some of websites I used to go on and implied this to mum and dad. I am not gay it was curiousity and dont know what to do