In my experience, anxiety tends to make us fear the worst in any given situation no matter how small the possibility. For me, counseling helped tremendously. Although anxiety may seem to strike out of the blue, there are often signs and 'symptoms' leading up to it and counseling can give you the ability to look into the fear you have of losing your family. I have gone through this (especially when my son was first born). The constant worry can 'eat away' at you, but first of all, you are definitely not alone in your experience with this. Second, you can confront this and deal with it quite successfully. As with any problem, the more knowledge we gain about it, the easier it becomes to deal with....keep us posted!
-- You may wish to consider getting on a medication that will lessen or possibly bring your anxiety under control. But the fact remains, that for whatever reason, you have developed a fear regarding something or someone in your life. Whether it is the fear of losing your parents, or some other family member, you are going to have to come to terms with it - by admitting and facing it. A combination of medication and counseling may work out for you - but I believe you absolutely need someone talk too about what is going on inside of you. Chances are it will not cure itself by ignoring it. Be proactive and address this issues a.s.a.p. Take care!!