I sing and play trumpet with tracks. Find in doing that I have some throat and sinus irritations. Recently I have been doing DJ work with some live work singing but no trumpet and I seem to have none of the old problems.
Will appreciate your experiences with this or similar.
I'm not a trumpet player myself, but I've known many over the years. The trumpet, like a number of other wind instruments, requires a significant amount of air pressure in the head cavity (mouth, throat, sinuses), and thus any type of sinus/nasal infection or mucus buildup is aggravated (worsened) by that "pressure" condition.
Some of the approaches I know they've tried are to not drink/eat dairy products before performing, stay hydrated (water!), take decongestants/allergy if necessary (one that doesn't cause sleepiness for you!!).
Jaw position is different for singing than horn playing. Your jaw is higher and more forward when playing trumpet. Your jaw is lower and more rearward when singing. On horn, you need a stable platform for your playing, but if you switch to vocal you need to let your jaw relax or you may get a strained sound (think Peter Cetera, the former singer from "Chicago"). While Peter can make that work for him, others may find that they do themselves vocal damage.
Practice going back and forth between the two. Sing for two bars, play for two bars, etc. Get some vocal lessons to find out proper technique.
Almost forgot... If you are using the same mic for both, you might have a problem.
Trumpet is louder than vocal. If the mic is turned up for singing (a hot mic) then it will be too loud when playing trumpet unless you back way off or play off axis. So you may try to turn the mic down because of this, only to find that you now have to "push" when you sing. You may not even notice that you are pushing until you are hoarse, then it is too late.
Solution? Two different mics. Or put a compressor on your mic to limit the volume when you play trumpet.