As long as a current (not expired) pharmacy label on the bottle matches the name on your identification, you'll be fine. Same goes for airports. We've never been questioned with any of the XYZ medications (including injections) that we have brought on holidays. No doctor's note necessary unless you are bringing large peripherals with you beyond what would be considered 'normal' carry-on luggage. (i.e. large amounts of paediatric formula)
It MUST have a pharmacy label!!! And when I say not expired, I mean the bottle has to have been filled recently and still contain the proper amount of medication (approximately; nobody is going to count). If you bring a bottle filled from 2007 and it says take 1 tablet daily for 30 days and you still have tablets in there, you could run into trouble.
You'll be fine.