Sometimes when I get anxious about something, I work to turn my thinking around and tell myself I am excited about that thing? After all, some things like roller coasters and watching horror shows, etc. are exciting because they are scary.

If I were in your situation, tearsinabottle, I would make "suggestion" and "invitation" mean the same thing. I would think that this friend and my sister care about me and want me to know that I have a friend whom I can visit if I want, that it isn't just my sister's friend but mine too if I want. Sometimes it is hard to go through change (your sister moving away) and start up, ask others for help or support? I think the friend may have been just preempting that and telling you it would be okay to visit, not that you "should".