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I would say, that when you say "keep on" you imply that she was already doing it, and she must continue.
However, keep going forward, sort of implies the smae thing, however, I think that, with the use of "on" it is given just that much more emphasis that she was laready doing it. But, the use of the word "keep" implies that she was already goind forward, but yeah..."on" just gives emphasis I think.
For "must" and "have to", they basically mean the same thing, but I think that "must" has more of a poetic feel than "have to", example, in the olden days, everyone always said "I must do this and this, etc" no one ever said "have to", I think that the invention of that phrase is particularly modern.
If the phrase is meant to sound more conversational, I would say, "I just have to keep on going forward." "Just" sounds better in front of keep, in all aspects I think, but I don't know the way in which her wording in Japanese may affect the placement of that word, but I would put it in front. It sounds less awkward than putting it after.
However, if you were to say "must", then I would say it the way martin did, "I must keep on just going forward."
"I must keep just going forward"...While people understand what you are saying...and it does make sense, it doesn't sound, natural.
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