these past months; for the last few months
Refers to the recent months leading up to the present. Often used adverbially with particles like は or この.
I've been busy these past months and can't seem to get a break.
These past few months I've been so busy with work that I could hardly rest.
I haven't been feeling well these last few months.
It's been rainy these past months, making it hard to go out.
近頃 is a common word for 'recently' without any month-specific nuance, whereas 月頃 specifically points to the last several months.
最近 is the everyday, broad word for 'recently', while 月頃 is a more literary term tied to a stretch of months.
先頃 refers to a single recent point in time ('the other day'), unlike 月頃 which covers an ongoing span of months.
Compound of 月 (tsuki, 'month') and 頃 (koro, 'approximate time'). The reading つきごろ is a straightforward combination.