Can I get a nose job with a newly installed palatal expander?

The best answers will be gotten from your palatial and nose surgeon. IMHO I would expand the palate first. Good luck

It is always best to have your dentist who performs the palatal expander discuss his/her treatment plan with your rhinoplasty surgeon. The palatal expander should not affect the shape of the  outside of the nose, but may have some affect on the septum, especially if it's deviated on the inside of the nose.

Best to have palatal expander doc discuss with your chosen nasal surgeon the relationship in concert of these two issues... 

You feel pressure in your nose because the palate is the floor of your nose. If the work is only being done on the outside of your nose, I don't think it should be a problem. If you have a deviated septum that needs to be repaired also, then I might consider waiting. The architecture of your septum may change as your palate is expanded, so better to fix it once instead of maybe needing more work down the road. Since the palate doesn't really affect the outside of your nose, I don't think it would be a problem. Good luck with everything.