Does having low blood sugar does mean you have diabetes?

No : Lower blood sugars are healthy. Problems with low(abnormal ) blood sugars sometime might predispose a person to diabetes later on but even that is a very debatable point.

Possibly: Many years before overt diabetes starts, someone at genetic risk can loss 'first-phase 'insulin release, resulting in an imbalance of sugar to Insulin levels 4-5 hours after eating, especially with simple sugars=sweets. Treatment is avoid sweets sometimes need to treat with dpp-4 inhibitors- safe, no undue side effects see dm specialist as most internists unaware of this.