You should be fine, but yes, bring copies of the prescriptions. If you have any critical medications (like if you stop taking things go bad) then I would get a letter from your Doctor indicating why he prescribed, dosages and the generic name of the drug. It would help if you dump your organizer across the floor of the train station, lose it, or otherwise cannot take the medication. Replacing requires going to a doctor there and having them prescribe what is needed.
If you take any controlled drugs (serious pain meds for example) or narcotics (for a variety of psychological ailments) those I would leave in their original labeled container, and have a letter from your doctor.
For all your medications, take only what you need, plus a buffer of a few days, don't take a 90 or 30 day supply for two weeks.
Whether customs wants to look into your bags is random chance, though it rarely happens; the good news is they are really not concerned about small amounts for obvious personal use.