I would ask for the following:
CBC with Differential = red cell count, white cell counts, platelets, parameters of red blood cells, individual white cell types & counts.
CMP = Comprehensive Metabolic Panel. Includes blood sugar, electrolytes, liver enzymes (AST, ALT, Alk Phos), Kidney function (Creatinine), BUN, protein, albumin, globulin, anion gap, co2.
Cholesterol - total, HDL, LDL, VLDL, ratios
Free T3, Free T4, TSH, Thyroid Antibodies
Fasting cortisol (must draw the blood as close to 8am as you can)
ESR (Erythrocyte Sedimentation Rate, or "Sed Rate")
CRP (C-Reactive Protein)
Autoimmune Panel (ANA w/ associated antibodies, RF, pANCA, cANCA, etc.)
Antiphospholipid Antibody screening
If they give you a hard time, ask for a referral to a Rheumatologist and then ask for these tests again.
Chronic Lyme Disease, Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication/Chemical Allergies & Intolerances, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD ("Secondary Lupus-Like Syndrome"), Osteoporosis, Pancytopenia, chronic malabsorption/malnutrition, etc.; G-Tube; Currently TPN-dependent.
Meds: Zofran, Pulmicort, Heparin (to flush PICC line), Claritin, Colloidal Silver (used topically), IV Milk Thistle, probiotics.