That will not be helping - could you go for a sweetener? I do not take them myself so cannot advise a good one.
Fluctuating sugar levels can be linked to headaches so it is possible that the sugar free drink results in a lower blood glucose level but I think it is unlikely to be acting that quickly.
Could you change to water for 48 hours so as to eliminate that as the cause? There is very likely a link between your blood glucose level and something you are eating or drinking, or both.
Diagnosed Type II 1998 1 x 80 mg Gliclazide, 4 x 500mg Metformin and 1 x 100mg Sitagliptin - HbA1c - 48 mmol/mol