Can Thrombosis Cause Swelling In Arms And Hand?

My father (age 70+ years) has heart blockage and he is staking medicine for last 14 years. Last 2-3 years, he is also suffering with Parkinson (that way he lost the balance in movement). Due to Parkinson problem, his movement is very restricted and slow. He is not able to walk first and not too long. This way his life has been going on. However very recently in one morning after waking up he has noticed that that there is some red patches in his right arm and it is also swelling and acing. One day later his also noticed that his right leg after the knee part, the muscle is very stiff and also acing. And the color of his right arm and right leg also changed. Based on the recommendation of the cardiologist, all the tests have been done (altra sonography, blood test, droppler sonography in legs). Dr. told that this is kind of Thrombosis due to which blood is clotted.. In between his hemoglobin ratio was dropped to 7. So for that purpose, 3 bottles of blood has been given to my father. The current condition is that color of hand/arm is becomes normal but swelling and aching is still there. Dr. has given some anti-biotitic. We are not sure whether treatment is going in right direction or not. Also we would like to know what may be reason for shelling in hand and arm and how we can overcome from it. many many thanks ...waiting to get some response ... Manab