Iam is very often used this way – it’s perfectly idiomatic. See the entry for iam in the Oxford Latin Dictionary. The particular usage you’re looking for is dealt with at 3(c) – ‘with expressions denoting extent of time or number of repetitions’. A few of the usage examples listed there are multos iam annos, uiginti iam annos and quartum iam diem.
The meaning here is ‘for two months now’, not ‘for almost two months’.
Also, your translation shouldn’t include the word ‘constantly’. The Latin has ‘prope cotidie’, which means ‘nearly every day’.