It is hard to tell the actual hue/color of the fluid on the dipstick, it does not look burnt from what I can tell, but again it is hard to tell looking at a small bit on the dipstick.
Does it smell really burnt?
If not yeah you still run a risk, but I don't think it will hurt anything myself, mine almost got burnt, and I had 4th clutch thrust washer parts in my filter, but a few thousand miles later it still shifts fine.
If you decide to change it I recommend some of this, it should help reduce the shudder you mention, use it once you change the filter of course.
A side not, I'd start saving up for a transmission rebuild, then once you have the money change the fluid, and see how it goes, that way if it improves you are good to go for a while, if not you won't be having to worry about getting the money together on such a short notice.