Hello
You should have a letter from your doctor/s with their contact details, saying what your diagnoses are, what medications you are on, allergies and any special considerations. That's as much for use in an emergency as for customs and security.
I have travelled transatlantic many times with no problem not even a questioning. I have no liquid medicines and nothing like syringes and no scheduled drugs. That advice goes for everybody regardless of nationality !
It depends on the quantity of meds involved but I have always taken a week's supply in carry on reckoning that if my suitcase was lost the most time it was likely to take to get it back was a week. However I am not dependent on any of my meds and don't have to take any regularly.
I would take all of any absolute essentials in hand baggage.
Some are now allowing two items hand baggage. Unfortunately an airline policy is not always consistent at each airport. I have had a weight limitation applied at departure point on way out, that wasn't any concern to the same airline on the return trip, where check in didn't bother about either weight or size of hand baggage.
You should also have a note in your purse or wallet in case of emergency with medications and diagnoses and allergies.
Check whether hold baggage should be left unlocked. You can do that at check in. It's no joke having a case ripped open and unusable even if the airline will replace it.
Good luck
Bee