It depends on whether you have sensitive skin or not. You shouldn't use the same mix all the time either, you should alternate so you don't build up a sensitivity to any particular oils.
To warm up your muscles i would recommend black pepper, ginger, peppermint, rosemary or juniper. Chamomile, lavender and marjoram are analgesic (pain relieving), so maybe a blend of black pepper, lavender and rosemary, or whichever mix you like, varying it so you aren't using the same oils constantly. If any of the oils cause a reaction, wash it off and stop using that particular essential oil.
I assume it's osteoarthritis, which is wear at the joint, rather than rheumatoid arthritis, which would be an autoimmune disorder and results in heat and swelling at the area.
Rheumatoid Arthritis Causes, Symptoms, Signs, Diagnosis and Treatment by MedicineNet.com. It appears that Baker's cysts are a complication of osteoarthritis
Baker Cyst Causes, Diagnosis, Symptoms and Treatment on MedicineNet.com
If it's osteoarthritis massage with essential oils can help to warm up the knee and also relieve pain. You could also try a compress with the oils. The oils i would recommend for this are:
analgesic oils benzoin, chamomile, eucalyptus, frankincense, geranium, ginger, lavender, marjoram, peppermint, rosemary
detoxifying oils black pepper, cypress, fennel, ginger, grapefruit, juniper, lemon, rosemary, sage, thyme
oils to improve circulation benzoin, black pepper, eucalyptus, garlic, geranium, ginger, lemon, mandarin, marjoram, rosemary, sage, thyme
So for a warming and analgesic blend for example, i would mix 1 drop benzoin, 2 drops black pepper, 1 drop of ginger and 2 drops of marjoram in 20 ml of a carrier oil e.g. grapeseed or almond oil or wheatgerm. This blend could be used before exercise and also to relieve pain and warm up the joint to help with the arthritis.
Your physio won't recommend any supplements because even though she will probably have learnt about them in college she will have been told that she isn't qualified or insured to recommend them. I suggest you ask your local pharmacist what might help you.