::Now I've checked the death date too. 22nd January is Old Style as well. The exact date of Shah Jahan's death is not in his own chronicle (which I am translating), but in that of his successor "Alamgir" Aurangzeb. In the Ma’āsir-i ‘Ālamgīrī, the author notes in the chapter on Aurangzeb's seventh year of reign, i.e. 1076 of the Hijra:

"Early in the night of Monday the 26th Rajab, Shah Jahan succumbed to the disease and gave up the ghost."
Sāqī Musta‘idd Khān: Ma’āsir-i ‘Ālamgīrī, tr. Jadunath Sarkar, 2nd ed. Delhi 1986, p. 34.
26th Rajab 1076 AH gives 1st February 1666 AD New Style and 22nd January 1666 AD Old Style. 
Date calculations can be done easily with the Swiss Calendar Converter, 
Greetings,