Welcome to the forum.
I'm sorry your girlfriend has been diagnosed with GD. She is going through a tough time and it can be a very hard time for those who love her as well.
You stated that she is taking her medications and I believe she is probably then also seeing a Dr. and getting the medical help she needs. I hope that is the case.
My personal opinion is giving her time to feel better and to actually have the strength to think about the relationship. I know that it is hard to do but you said you love her and she said she needs space and time and therefore, since she has asked for it, I think you should give it to her.
Before she leaves, let her know that you love her, let her know that you made a mistake but that you have corrected it by getting informed about the disease and joining a support group, let her know that you will be there to support her when she needs you. Give her time and don't concentrate on how her diagnosis/symptoms could have added to the arguments because that is the last thing she wants to hear. You have mentioned it to her and there is nothing else you can tell her about it. Give her the support she needs by letting her know what I mentioned above. Well, that is just what I think might be appropriate at this time since she has asked to be left alone. Only you know the situation and only you are the best judge to decide what to do. Her health is the most important thing at the moment in my personal opinion.
I believe that time will be your friend on this one. As long as she is taking care of her medical needs I think you should support her by giving her the time she is requesting. There is no worst feeling than feeling sick and having to deal with a lot of other things around you. The best thing my husband has said to me is that he is and will be there to support me. Daily hugs and daily understanding is a big plus …. especially at the beginning when we are trying to learn how to cope with everything. Believe me, this disease makes us feel very very sick. I know that I have had to give it my all to carry on with my life and deal with the disease. It is not easy on anyone. I know that the less I had/have to worry about at the moment the better. Your girlfriend might be thinking the same. I'm also new with the whole thing so I'm still learning how to cope with it all.
I'm glad you have joined us. You will find support here. I hope with all my heart that your girlfriend will soon feel a lot better.