I don't think it should stop you from traveling, as long as you have a passport allows you to enter your destination.
 
	 
 
	Oath ceremony depends on the FO, some donit in 3 weeks, some up to a month, some more, others in some states do same day. It's really unpredictable.
 
	 
 
	For passport, I've read in the forum that when expedited takes 2 to 3 weeks for urgent travel happening within 6 weeks.