Surely the other kid would have it and the parents too if it was all over the house and they were unhygienic and had no soap.
I think your anxiety is causing you to freak out and the physical symptoms are tying in with the anxiety.
Try to stay calm and rationalise that there's not much you can do except wash your hands before you consume anything. Other than that you will carry on as normal and if it happens then you will deal with it.
I would be very surprised if you got sick