Do you notice an increase in this usage lately? I see it a lot on reddit and hn. All romance languages probably have it by the way. I know Italian does for sure.
You could use it in English too so long as you add 'ago' on the end. "Since two days" makes no sense in English because "since" refers to a point in time not a duration.
That still doesn't sound natural to me. You could answer 'since when' with 'two days ago', but declaring it as a statement I'd say 'for the last two days' or 'since the day before yesterday'.
You could get away with it in speech since it sounds like 'since.. [thinking] two days ago' and it's acceptable to change construction like that in casual speech, but written it doesn't seem right to me.