Hi Kitty, some people with FM report having nausea some of the time. It's pretty hard to say whether yours is or is not a part of FM, though.
Since this is a new symptom for you I would suggest waiting to see if it is something temporary and will go away. If it doesn't go away in another week or so, please report this to your doctor. Any new symptom that is not just temporary should always be checked out by medical professionals, because it could be something other than FM and you really need to know. I don't know why you are sure it is not a gastro bug, having only had this for a week. I have had gastro-intestinal illnesses that lasted a lot longer than that.
In the meantime, I would take a good look at what you are eating, do all you can to reduce stress in your life, try to get as much sleep as you can, and take a ginger tincture, which is sometimes helpful with nausea.
Personally, I am ultra-familiar with nausea, having had chronic nausea for many many years. Turns out for me going gluten free solved that problem, along with some others, by about 90%. There may be something that you can do to change this, but I wouldn't get too caught up in it until you determine whether this is a long-lasting thing for you or not.