The duplication of “thought away” is a mistake in your edition of the poem. The line should read:
That she was as old as she looked, but soon
See for example, Mary Ann Dasgupta, ed. (1978), Hers: Indian Perspectives, page 29, which is available in Google Books “snippet view”.
I do not know where the mistaken edition comes from, but it seems quite widespread. The mistaken version of the line makes no sense, which ought to be a clue that something went wrong.
Are all interpretations valid?
I’m not keen on this way of putting it, because something is either “valid” or not. This is fine when you’re talking about mathematical proofs, but interpretations of poetry aren’t binary, black-and-white, in that way.
So I think it’s better to ask about an interpretation how convincing it is (that is, how much sense it makes and to what extent is it backed up with evidence from the text), and how useful it is (that is, how much it helps you understand and appreciate the text).
In this light, one interpretation can certainly be more convincing, or more useful, than another.
She is trying to exaggerate in a sense, by over-using the word smile.
If the speaker is trying to exaggerate, this means that she didn’t smile very much, but is trying to give someone the false impression that she smiled a lot. But who is she trying to deceive? In the “smile and smile and smile” line, the speaker does not seem to be talking to anyone other than the reader of the poem. But if she is trying to deceive the reader about how much she smiled, what else might she be trying to deceive the reader about?
This is a general problem of interpretations that suppose narration to be unreliable: once you start to consider the possibility that the narrator is not always telling the reader the truth, then it is hard to know where to stop. For this reason most readers prefer not to entertain the possibility unless the text is very clear about it. (I wrote about this problem in more detail in this answer.)
She wanted to hide her feelings of sadness.
She wanted to hide her feeling of sadness from her mother, not from the reader of the poem. But the “smile and smile and smile” line is addressed to the reader, not to her mother. So this interpretation does not explain the repetition of “smile”.
She was out of words.
I can imagine the speaker not knowing what to say to her mother, because her thoughts are sad and she does not want to say anything in case she gives herself away, so all she can do is smile, and the repetition of “smile” suggests how long this went on.
(My own interpretation.) The repetition conveys how difficult the speaker found it to smile. She feels “that old familiar ache, my childhood’s fear” (that is, the fear that her mother will die), but she does not want to reveal this fear to her mother, so she smiles instead. But smiling is hard when it does not come naturally from one’s emotion, and so she has to consciously tell herself over and over to smile, in case her concentration should lapse and her feelings reveal themselves.