The Usage of "Like Anything"
Solution 1:
I have become familiar with the expression like anything as a general intensifier through Indian English, where it seems to be used very often - I have not heard it used regularly in any other dialect, which doesn't mean it is not used at all.
However, that does not mean I agree with Jonas' comment that therefore it should be avoided. As an intensifier, it is readily understood, also by people that have not heard it before, and it is certainly an established expression in what may be the fastest growing, and soon-to-be most-spoken, dialect of English.
I expect native speakers of Indian English to use this expression, as well as other particular expressions that adorn the Indian dialect of English.
It certainly causes less confusion to speakers of other dialect than the British use of a rubber - or for that matter, the Indian use of bottom to mean the lower part of one's clothing.
Solution 2:
OED covers the usage under like sense B 1b...
In colloquial phrases denoting vigour or rapidity of action, as like anything, like a shot, like fun, like blazes, etc.
They have citations going back to 1681 with like any thing, but it's not until 1871 that we get the single-word version, in Lewis Carroll's Through the Looking-glass...
In short, the usage is long-established, and has no particular associations with "Indian English" or any other regional dialect. But it remains rather colloquial/informal.
Solution 3:
I heard "like anything" from my father, whose family came from rural Iowa. I think I've also heard "like everything," but I may be mistaken. I used it myself just the other day (I grew up in southern California in the 1940s-50s, but I've always assumed it came from my midwestern roots.)