Thanks for your query at DoctorSpring.com
These diseases are rarely seen in the USA, and it is always a risk flying out to a new destination without recommended vaccinations.
Now the catch is that you are totally allergic to these vaccines.
So there is no question of receiving these vaccinations.
So yes, you can fly out, with a calculated risk.
Flying itself is alright as long as it is not a very long distance flight, and you get an aisle seat and walk about every 30 minutes or so.
Hydration also is critical for air travel.
All the best.
Please feel free to discuss further.