I have just been prescribed Montelukast, will this help with inflammation, Rheumatoid arthritis?

No Montelukast won't help with inflammation due to rheumatoid arthritis.

Montelukast is a leukotriene inhibitor. Leukotrienes are chemicals your body releases when you breathe in an allergen (such as pollen). These chemicals cause swelling in your lungs and tightening of the muscles around your airways, which can result in asthma symptoms.

It binds to cysteinyl leukotriene (CysLT 1 ) receptor in the upper and lower airways to prevent leukotriene-mediated effects associated with asthma and allergic rhinitis. So it very specifically works in the lungs.

Montelukast is used to prevent asthma attacks in adults and children as young as 12 months old. It is also used to relieve runny nose and sneezing caused by allergies in adults and children as young as 6 months old.

http://www.drugs.com/mtm/montelukast.html

http://www.drugs.com/ppa/montelukast-sodium.html