Need to reset my icloud password but it's complicated

So this is going to sound very stupid. Try to forgive me. I can be extremely paranoid at times! Anyway getting on with the question....

I had to reset my iPad because I had forgotten the password. I then realise I have to activate it using my icloud account. This was because I had recently added Find My iPhone to it. This would have been fine except it had been a while since I made the account and now I'd completely forgotten the password. I went to reset the password online but when I asked them to send me an email with the reset link I couldn't find it anywhere. I looked through spam but it wasn't there either.

I tried to reset it using the security questions instead. The first question was the problem. I had to give my birth date. This would be fine except that I, being the paranoid person that I am, had put in a completely random birthday. I have no idea what it is and now I can't reset my password. I even put in a fake name. I think I know what it is though.

If anyone has any idea what I can do it would be greatly appreciated. I'm locked out of my iPad at the moment and would dearly love to have access to it again. I was going to call apple support tomorrow but thought I'd run it by you guys first.