Check in on or checking on?
They are both correct phrases. Apparently "checking on me" has an older lineage, but in modern English, either is appropriate (in the US anyways).
"Checking in", it could be argued, has a connotation of the speaker being physically present, as in someone coming to visit or a parent or nurse looking into your room. However, the distinction is small enough to be irrelevant — no one I know would fault you for using it in a letter.