My 2 cents –
I drank cow’s milk kefir and had the same reaction very intense - not a fever though - but streaming nose and blocked ears. Terrible, terrible reaction and too much to be dieoff. I had to go to a doctor to get my ears syringed.
I tried everything - I did 12 hour kefir and 24 hour kefir (to get rid of the sugar/milk). Finally I just drank the whey (more or less water) from making kefir cheese. I even tried kefir with raw milk.
There is an opinion that parasites feed off probiotics and, with my history of parasites, I have never been able to take them. I have tried Bio-acidophilus, Threelac, Kefir, fermented veg. You might find you are in the same boat.