After lighting weights is there any specific muscle group which remains sore or is your overall upper body sore ? How much weight are you lifting now ? Are you doing bench press or deadlift ?
My upper body workout usually contains bench press, push up, pull up, wrist curl, shoulder press, triceps extension and bicep curl. This pretty much covers my entire upper body. I usually do three of the before mentioned exercise in three sets with varying count - 10 reps, 12 reps, 15 reps. On days when I am already exhausted I reduce the sets to two with same reps. I am working with a physical fitness trainer since I am trying to lose some weight as well, so some amount of cardio/aerobic exercises get mixed up in my workouts.
I usually do my workout on Monday and Wednesday leaving ample time for my body to recover for the weekend game. The day of your workout and the next day - reduce carb/sugar intake and increase your protein intake. Combine this with stretches and you will see a quicker muscle recovery.
I don't see any problem in lifting weights during your cricket season. You should choose weights which helps strengthen your muscles without the loss of muscular flexibility. If you are lifting weights which are too heavy then it will make your muscles very stiff and longer recovery from soreness. Gradually increase the weights ...