Are there any rules for taking medication with me? Like do I need to bring a doctor's note with it or just the bottle?
There has been lots of discussion on this point. Simple, put it in a plastic bag. Leaving the country, nobody, least of all TSA security, is concerned about quantity of pills. If it is a controlled medication you probably should have a doctors Rx or the original bottle on returning to the US for the most unlikely event that a custom agent might ask two questions. By the time I return my plastic bag of pills is down to a few so it is not significant. You should carry the generic name (not brand name) of your medication if you need to obtain extra in Europe should you lose or misplace your current supply.
Spikefan,
Frank has given you sound advice.
You can take medications with you without any issues.
Make sure you take them in your carry-on.
Bring extras with you, just in case...
You may want to refer to the TSA website for more information: http://www.tsa.gov/traveler-information/what-expect-if-passenger-needs-medication
And definitely take several days extra with you. You can't anticipate cancelled flights, strikes (very rare; don't panic!), volcanic eruptions, etc. They also have a talent for sliding down the sink drain, rolling behind the headboard...