Lymphoma can present that way. ask you doctor to do a blood test called beta-2 microglobulin - this is often elevated in lymphoma. If your insurance will pay for it (around $2000), a PET scan would be a good idea. Lymphoma and other cancers light up like a Christmas tree on a PET scan. If you have lymphoma, and since you have had symptoms for so long, there is a good chance the lymphoma has made its way to the bone marrow. Therefore, a bone marrow biopsy would not only confirm the diagnosis if positive, but it could be checked for CD20 receptor status. Rituxan is a great drug for lymphomas that are CD20 positive. Generally, bone marrow biopsies are done by oncologists, so ask your primary care doctor for a referral to one. They usually have a better track record for getting PET scan approval by insurance companies, so asking for a referral to an oncologist is not a bad idea at all.
There are lots of other things besides lymphoma that it could be. A consult with a gastroenterologist, an EGD, a colonoscopy, maybe a CT or MRI of your abdomen all would be a good idea.
Eosinophils usually mean you are being exposed to something you are allergic to. Low iron stores usually mean you are not replacing iron lost with menses, but can also mean bad things like gastrointestinal bleeding (polyp, ulcer, cancer etc) or bone marrow suppression. Shortness of breath can be due to the anemia, or heart disease, but if I had to guess, I would guess it is asthma since your eosinophils were elevated too at that time. Seeing an allergist for allergy skin testing is not a bad idea.
There are other things it could be, like autoimmune diseases, or metabolic diseases, like Wilson's disease, but I think a good start would be the things mentioned above.
Just my thoughts.
-Amnia