This can happen if you do something like this:
Your data plus the vector of the month:
y <- c(23, 34, 11, 9.6, 26, 31, 38, 38, 30, 36, 31) days <- seq(as.Date("2015-2-25"), by="day", length=11)
Decision:
plot(x, y, type='n', xlab="Days", ylab="Y", xaxt='n') axis(1, at=seq(1,11) ,labels=format(days, "%d"), las=1) lines(y)
Before that, only your code. Now you need to add a new axis, set the axis color to white and build the month vector created above:
par(new=T)
The result looks like you requested:

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