I would tend to agree with you. What type of doctors have been telling you about the SI dysfunction? Maybe the fluid is a result of your fall and it is pressing on a nerve. It is also possible that the fall has caused swelling. Does icing the area have any effect?
My SI joints are hypermobile and fairly frequently one side or the other will slip. This allows one side of my pelvis to rotate slightly forward. This can cause some "congestion" in the tissue which is similar to swelling and it can put pressure on the nerve. It can be a vicious circle...once the swelling starts it makes the nerve compression worse. This causes me to favor that side, which throws off my gait and creates other issues, etc....
Have you tried wearing a SI belt? In the beginning that helped me and I know others are able to walk better and further when using one. I currently go to a guy who does acupuncture to relax the tissue and then he does very gentle adjustments. I have also had to train myself to sit squarely with even pressure on both buttocks, with feet flat on the floor and legs uncrossed. Otherwise, for example, when legs are crossed, I favor one side, and it makes the pelvic rotation worse....Same when standing. I used to stand with more weight on one foot than the other with that hip somewhat out to the side. I've had to learn to stand with my weight equally distributed between my feet....these are small things, but when repeated over and over each day for a lifetime, it makes a difference!!
It could be that a tight piriformis muscle is causing your sciatic pain. Do you do stretches to keep the piriformis loose? The sciatic nerve runs right underneath the piriformis muscle. In some people the muscle is particularly well-developed...this can cause sciatica that affects the buttock and the leg...as can a spasm in that muscle. Someone like a physical therapist, or therapeutic massage therapist can often tell you if the piriformis is to "blame" for the sciatic pain. You can read up on piriformis syndrome if you want to learn more. Hope you find some answers soon!