As far as I know Princess Alice of Battenberg was deaf from the very beginning as her auditory passages were too narrow - I did not read something about scarlet fever yet.
What I read in "Advoce to a grand-daughter" is that she learnt to read from the lips in four languages when aged 15...English, German, Frensh and Greek
From Hugo Vicker's Alice:
p.24: No one had yet noticed that Alice was deaf. The first hint came in a letter to Queen Victoria in January 1887, though the cause was still underdevloped in her mother's mind. Victoria wrote:
'Baby looks so nice in the pretty frocks you gave her. She is very slow in learning to talk, but on the other hand very clever with her fingers..."
p.25: It was not until Alice was four yers old that her mother began to articulate her concern. In a progress report to Queen Victoria she wrote:
'The child has grown very much since last you saw her, is very lively & quick with her fingers, but decidedly backward in speech, using all sorts of self-invented words & pronouncing others very indistinctly, so that strangers find it difficult to understand her. We make great efforts to improve this & I think the society of her little Erbach cousin is helping her on.'
Alice's grandmother, Princess Battenberg, was the person who identified the problem as deafness, taking Alice to an ear specialist in Darmstadt. Alice had been born with the defect, though some in the family assert that her hearing was damaged on one of her early sea voyages. The deafness was due to the thickness of the Eustachian tubes and would always be a problem. Her mother spent long hours with her, teaching her to lip-read, and she learned to follow conversations. By May 1889, Alice was speaking 'quite nicely at last', and her hearing was deemed better a year later. But in 1893, when she was eight, Victoria took her to an aurist in London, her lacak of progress remaining a 'great worry' to her parents. They discovered that no operation was possible. By the age of fourteen, there was a marked improvement, but it was not until as late as 1922 that Alice announced that she had heard a cuckoo for the first time. The deafness isolated Alice from the usual friendships of childhood but she learned to fall back on her own resources....Her mother had to decide how to treat her within the family circle. Alice's yonger brothers and sister were told that they must talk normally amongst themselves, making no concession to Alice. She would either join in or not....As she grew older, Alice could hear certain voices according to pitch. In the 1950s she surprised her family in Baden by hearing the guards march outside. It was the echo of stamping boots that she detected. And her lip-reading became so good that people put their hands over their mouths when imparting secrets across the room, aware that she could lip-read not only in English and German but in several languages. 'You had to be very careful what you said,' recalled Alice's niece, Princess Eugenie. [Footnote: Many years later Alice relished watching silent films, where she was able to lip-read what the characters were really saying. She amused her family by relating how in a passionate love scene in Von Stroheim's film, Greed (1923), in reality the hero was telling the heroine that he was being evicted for not paying his rent.]