Hi Sunil, if this is causing you some serious pain you might not be best off only obtaining advice from here. If it is still persisting after two weeks of rest and a little intervention, go see a doctor who may help you get back on track a little quicker.
If you are just starting out, especially from a relatively sedentary lifestyle, you should ease into the routine slowly. If the you are unable to stretch your calf when the pain happenes, it could be cramp. This needs rest, stretching and massaging (take care not to apply pressue on varicose veins). If its microtrauma, the pain might be more sharp and focused to a point in the muscle. This also needs rest as continuing exercise will lead to more injury.
Give your body a little time to repair itself and keep your calves, hamstrings flexible. When you are back to your routine, look into doing more core exercises especially those which work the transversus abdominis (squats, deadlifts, lying leg raises, lying bicycle, trunk raises etc.). These may help you sort out any posture and strength imbalances which lead to injuries like this.
You mention doing one body part a day in your weight training. I assume from this you are perhaps doing a lot of isolated exercises and open chain movements? I did a quick google search on this for you, you might find it interesting...
http://www.healthline.com/hlbook/art-open-chain-versus-closed-chain-exercise If you are just starting out with the weights, I would suggest you make sure you are following a routine which focuses more on axial training (working muscles close to the spine, pelvis and shoulder girdle) rather than peripheral training (like biceps, triceps etc.). This would be using the squats, deadlifts, rows and overhead press. They work all the major muslces in a more functional mannor which better assists everyday life activities. It is harder to form muslce imbalances with these too as compared to overworking a bicep in comparison to the tricep which beginners often dont realise that the relative strenght difference should be the other way around.
I have to go prepare a 1.8 kilo roast. Feel free to put out any questions you have on the forum.