Your story sounds like mine, but my incoordination was almost completely eye-hand and did not affect my lower limbs. With this being the case I was terrible at sports except for dancing and running, and in the latter I excelled! I never could put a puck, a ball, or a bat anywhere near where it was supposed to go, but I was otherwise so healthy that teachers and parents and doctors wrote it off. I was, of course, accused of having mental problems--particularly not wanting to socialize--when I could not play baseball no matter how hard I tried in the fifth grade. But I did so well at dancing in various public venues that everyone thought I was impervious! I got a D in Archery and a D in bowling in the mandatory college courses, and nasty looks from the teachers.
My parents, I realized later, were scared of what lurked, the dread MS gene which was supposed to be ruining the life of my father's sister, who had been a math teacher at Lincoln High in Portland Oregon, and an organist at the church founded by her father and his brothers. My mother said that Lucile fell down in "every doorway of Meir and Frank" department store. My mother said this with horror.
In college I got sick, but the problem was not so much balance then as other symptoms, tachycardia, abdominal pain, radical constipation. I wasn't taking a sport other than dancing, so it didn't show up so much, but the Health Service could think of nothing except psychological causes. Decades later I was dx'd with Porphyria another neuro disease which could explain the college difficulty, but first I was dx'd by more than one doctor with MS, including Dr. Swank, the author who used his special blood test on me as well as accepting another doctor's more usual diagnostic tests. I learned later that some people at Swank's institution (OHSU) think that some people who have Porphyria or MS may actually have both things, but diagnosis is so difficult in any case that it would require the type of medical care of, say, the President of the United States, or the Kennedy Family, to get a clear dx of which was what. In other words, as you hinted yourself, diagnosis is difficult. I have come to accept both diagnoses as valid. After dx with Porphyria I was able to avoid triggers and did better, but my neurological impairment from "whatever" is still with me. I have done very well, perhaps because I have sought alternative treatments such as Dr. Swank's. But my youth was clouded by the unknown disease, which was a threat or a killer of family relationships--prior to marriage to my great second husband.
Now I have the numbness in the feet, and must be very careful not to trip, so I now have your lower extremity difficulty too. So life is led very carefully.