Raising Door Frame On Load Bearing Wall
I had a similar situation recently and here's what I did. Disclaimer-there might be better ways to do this and I suggest you wait on more answers or comments.
I created a temporary header near the doorway using 6x6's on the ceiling and floor, with bottle jacks and studs to hold the system up. I used foam board on the ceiling to not damage the drywall finish. Once everything is in place I slowly cranked up each bottle jack a little at a time until I could tell I was getting good pressure on the ceiling. If you go this route, you need to verify which way the floor and ceiling joists run, so that you can distribute the load. If you have trusses, make sure you put this on the side of the wall that keeps it under the truss. You will need someone to help get you get this set up, it's difficult to hold everything in place while working the bottle jacks.