You can work arms every 3 days, but why? You won't get better results, just tired arms. I think you're absolutely right about your lack of strength gains: it's during the recovery time that muscle rebuilds (bigger, stronger, leaps tall buildings) not during your workout. No rest = no recovery.
My suggestion is to either try the classis BFL split:
Week 1: Upper body, Lower Body, Upper Body
Week 2: Lower, Upper, Lower
Do cardio on days 2,4,and 6, rest on day 7
Repeat 2 week cycle.
or
Do the split I suggested in the above post, each week with cardio on days 2,4,6, and rest on day 7.
I don't know what condition you are in, your age, how long you've been lifting, etc to make any more specific recommendations

Personally, I like a 4 day split, and have occassionally done a 5 day split- but you have to really love the gym to do that.
Hope this helps,
mel