Gosh, parasites. Ugh. Had one myself along with my husband and son after a trip to a farm and eating fruit washed from the tap which was contaminated. I lost a lot of weight! I feel for you.
So, from my reading, Amoebiasis is a heading for all parasites/organisms found to cause infection from any of the amobae of the Entamoeba group. So this includes entamoeba coli (you ARE talking about the parasite and not bacterium, correct?). Here is some information about it https://www.emedicinehealth.com/amebiasis_entamoeba_histolytica_infection/article_em.htm.
The main thing you need to ask your doctor is if treatment the same regardless of the amobae? I assume it is. I have read though that patients are often treated with a first antibiotic and then a second for full treatment and with your symptoms, would think this is the case for you. So, do follow up with your doctor. Also, it is really important that you figure out the source of where you got this if you can. We knew. Why? Well, unfortunately about 70 other people at the family reunion also got the parasite. My son had a different parasite and the health department actually decided the source was feeding ducks at a pond in a park where others had gotten the parasite (duck poop on things on the shore he had likely touched). Yours may be more water related--- if you haven't drank unsafe water, think in terms of like us, fruit washed in unsafe water, ice cubes, salad washed in unsafe water, etc. But this is also contagious so be vigilant with your hand washing after going to the bathroom. I'm sure you are.
good luck and let us know what your doctor says!