Try chewing gum and sucking on hard candy as the above poster mentioned. Also, try to move your jaw and yawn frequently; this will help equalize the pressure in your head via your ears. You can also ask your physician about recommending a decongestant, i.e. Afrin spray, for you to take prior to your flight. This will open the nasal passages and ears thus relieving pressure.
Gum, chewing gum once the flight is about to take off helps with the ears. I also try to take a cozy travel pillow and small throw along with me along with taking slow relaxing breaths. If you have an ipod and/or headphones with music or a book to listen to it helps to drown out the noises of the planes and other passengers.
This may be a dumb question, but can you get to NY without taking a plane? If not, then I'd suggest making an appt. with the doctor who prescribed your paracetomol to see about a replacement med for it. You might also try learning deep relaxation exercises, which help some people with migraines, panic attacks, and such, but it generally takes more than a week to get good at these.