It's a matter of opinion about aspartame, I don't worry about it and many don't, but just as many don't like it. I use lemsip when I have a cold, I find them comforting and they don't really affect my BS, although you may find that being ill affects your BS anyway, I have found this link for you and an extract of what it says so you can decide for yourself (my bold)
http://www.medicines.org.uk/emcmobile/medicine/23353/spc
Use with caution in patients with hypertension, heart disease, diabetes, hyperthyroidism, hyperexcitability, phaeochromocytoma, prostatic enlargement or close angle glaucoma. Each sachet contains approximately 2.1 g of carbohydrate. Care is advised in the administration of paracetamol to patients with severe renal or severe hepatic impairment. The hazard of overdose is greater in those with non-cirrhotic alcoholic liver disease. Patients should be advised not to take other paracetamol-containing products concurrently.