Rain will dilute all levels some but not significantly.
You are right that if your numbers are ok you usually don't need to shock. But, your numbers are not ok. You have a CC reading of 2 and you want it to be 0. The way to lower the CC is to shock the pool. How high to shock depends on what your CYA level is. If you haven't yet done so, please read the Best Guess Chlorine Chart in my signature below.
So what you need to do is to shock the pool up to a chlorine level of 15ppm. In your pool, each gallon of plain, unscented 6% bleach (generic is fine; most of us use generic Walmart bleach) will add about 3.7ppm of bleach. Use that as a reference to help you figure out how much bleach to add each time you test. You'll want to keep the chlorine level at about 15 until you can go from sundown one evening to within two hours of sunrise the next day without losing more than 1ppm of chlorine overnight and you have a CC reading no higher than 0.5. At that point, I would suggest keeping the chlorine high for one additional day and then let it drift down and keep it between 3-6 all the time.
(Once you get past this, I'd suggest bumping your CYA up a little to get it up to about 50. You can use trichlor pucks for a little while and monitor your CYA level every couple of weeks.)
Hope this helps.
EDIT to add a link for you to read which may be helpful.
http://www.poolforum.com/pf2/showthr...-Abbreviations
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