Question about signing on the sick? (UK)?

Ok I was made redundant last september, so i signed on for job seekers allowance. the following november i went to my GP after having some discomfort in my left side. he sent me to hospital where they diagnosed me with Essential Thrombocytosis, a rare bone marrow disorder. I was told that this a lifelong condition and also that i would have to take Hydroxycarbamide which is a chemotherapy drug for the rest of my life. Anyway as soon as I started taking the hydroxcarbamide i began to feel fatigued and weak. i told my consultant this and he lowered my dose but i still feel the same side effects. I carried on signing for my jobseekers allowance because i felt i could still work. However recently the fatigue and weakness have been getting worse. So i applied employment and support allowance instead. They told me that i would need a sick note from my GP. However i have not been seeing my GP about the condition i have been seeing a haematologist at a hospital. My GP has been honest to admit that he does not know much about this condition. So who do i get my sicknote from? my hospital DR or my GP? Would they refuse it for any reason? I have no physical disability but the drugs do make feel terrible and the Dr said i cannot stop taking them.