Melbourne weather is horrible. Four seasons in one day. It is the classic of Melbourne. Melb also is a garden state. It full of pollens. You get hay-fever and it affects breathing as well.
Well, those are just the landing experience. Aeroplane is air and pressure controlled. You shouldn't experience these. They spread anti-germs in the aeroplane before the plane opens its doors. Too bad, if you're allergic or not, you got no option. You definately can take an allergic tablet before they spread.
I get those sensation when I have the bundle branch block. I have both right and left BBB. But this is just me. Everyone is different. As Ed34 said, it could be the development of blood clot too. Check out at one of the hospital while you're arrived. Most of the public and/or private hospital operates 24 hours at the emergency department. Anyone can walk in but just don't know how long should be sitted at the waiting area. The triage nurse will category your urgency level. Sometimes I got in to see a doctor in a few minutes, sometimes I got to wait at the waiting area for 6 hours long. It costs a lot though if you didn't have the insurance covered. Take care and good luck. Welcome to Melbourne.
I dont know how far you flew to get to australia, but Im guessing it was quite a while on a plane. You could have a simple blood test to see if you show any signs of developing a clot from the flight. It just seems a coincidence that you are getting these symptoms after the flight. Aspirin will help to a small extent but will not be enough.
The environment can also affect you, especially climate. Is it a lot warmer in Australia than you are used to? I would drink plenty of fluids.