Heparin doesn't break up existing clots, it just slows clotting. If you're concerned, you should have a discussion with your doctor about the bleeding risks of being on the Heparin.
Vitamin E, Sassafrass, NingXia Red (Ningxia wolfberry juice), and some other things can help with thinning the blood naturally. Make sure you don't get dehydrated...that makes thick blood worse in my opinion.
Inflammation causes thickened blood also, so any anti-inflammatory herbs should also help (tumeric, ginger, boswellia, bromelain, etc.).
Chronic Lyme & Bartonella, Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication/Chemical Allergies & Intolerances, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD ("Secondary Lupus-Like Syndrome"), Osteoporosis, etc.; G-Tube; TPN via PICC (trying again to wean off the TPN).
Meds: IV Cipro, Heparin (to flush PICC line), Singulair, Claritin, Domperidone, Colloidal Silver, probiotics, digestive enzymes, Milk Thistle & other liver support herbs, Magnesium, Progessence+ (wild yam + essential oils), Moducare, homeopathy.