If you do that schedule, well, just check out the link to the photo of your future results.
A sponge with huge arms.
You need to be working all of the muscles of your body, not just the arms. You have a body not a collection of individual parts. Since you want to lift 3 days a week, try something like this:
Day 1 - legs/arms
Day 2 - cardio
Day 3 - rest
Day 4 - shoulders/back
Day 5 - cardio
Day 6 - rest
Day 7 - chest/abs
This may not be the most optimum way to do it, but it is better than only doing arms 3 days a week and not doing the rest of the body - and it fits with your cardio/rest schedule.
For legs do something like squats/stiff leg deadlifts/calf raises. Arms you could do bb curls/skull crushers/db curls/tricep pushdowns
For shoulders there are things like seated bb shoulder press/seated db press/shrugs/upright row. For the back there is the deadlift/bent over row/pullups (or lat pulldowns if you can't do pullups yet).
For the chest there is the
flat bench press/incline bench press/decline bench press/dips. Abs there are floor crunches/decline crunches/seated cable crunches/kneeling cable crunches/variations of the crunch with weights on your chest or behind the head. Don't forget the ab-roller type exercises either.
Pick a two or three for each body part. Do 2-4 sets of 4-6 reps, 6-8 reps, 8-10 reps, 10-12 reps...whatever you prefer and do them on the appropriate day.
Have fun and make some progress.