Yes you may. Your shawwal fast is only connected to this Ramadan and not the previous ones.

I still have some fasts from previous ramadans to make up, can i make them up after my shawwal fasts or will my shawwal for this year not count unless i make up all my missed fast from the past? Also am I allowed to make up my fasts in the winter when the days are shorter or is that seen as less rewarding because the days are shorter?

Fasting | May 29, 2017 4:45 am
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We are having a doubt on when to stop suhoor here in Germany as muslim pro app shows fajr at 3 am but sunrise is at 5.25 am and dawn in our city as per google is at 04.38 am … and the turkish community stops eating at 1am …. very confusing SobhanAllah. Please advise us
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sheikh i frequently suffer from headaches and rely on painkillers to help with the pain. Would it break my fast if i was to orally take paikillers with a little bit of water? if yes can i take it more than once during the course of the day?