I couldn't agree more.
It's awfully presumptuous of him to insert himself into such a personal and private decision. I don't blame you one bit for being upset, offended, irritated and now nervous.
I think getting your own computer is probably a really good idea if your brother is unable or unwilling to respect your privacy.
I know I wish I had started trying at your age... if I had, there's a chance I wouldn't be having to take fertility meds and all of that. For that reason alone, you shouldn't have to justify your choices to anyone... nor should you be forced to explain concerns about waning fertility in later years to your 20 year old brother.
I hope that things are able to smooth out for you and that you and DBF will have a place of your own very soon so that you can truly have some serious privacy.