I use the small Ziploc type bags (Rite aid carries them in their travel section) to hold each of the pills, then put them inside a larger baggie to organize (hubby’s prescriptions in one, mine in another, and otc’s in a third). Takes very little space.
TSA does NOT require that meds be in original bottle or label. Whether or not inspectors in other countries will worry about how you have your pills organized is always a question. Personally, I've never had a problem taking meds into other countries for my personal use (and we've had more than 40 international trips)
It is the INFORMATION that is important- more in case you have a medical emergency, or need a refill (lost meds, trip extended...) You should have the brand name of the medication (ambien, etc.) and the generic name, and if no generic, a "chemical" name as brand names are not always the same.
There are lots of ways to organize your meds. You can ask your pharmacist to print you an extra label (or use the one they give you that is with the 'side effects" printout) and put it on a small Ziploc bag, then put the medication in the bag. Alternatively, some pharmacies will prepare blister packs with all your meds grouped according to when you take them (example, day 1, am in one blister, day 1 lunch next, day 1 pm next, etc)and put all labels on the top of the sheet. You could use a pill organizer as you've mentioned, and put the labels from the pharmacy on one sheet of paper with the organizer.
I carry an information sheet with the above info (one for me , one for hubby)and I also list my Dr's phone #s, pharmacy's #, and emergency contact info as well a list medical conditions, surgeries /dates. If you become ill while traveling, or need a refill because you lost meds, etc. it could be vital. Feel free to private message me if you want a sample copy of the info sheet.
Also, note that liquid meds of more than 3 oz should NOT be placed in your 3-1-1 bag, but should be in their own baggie, and this is one time where an 'official' label is helpful. Diabetic supplies that include sharps (needles, lancets, etc.) should be bagged separately and declared when you get in line at the TSA security point, also.