My vagina is very tender and itches. No smell or has a pinkish duscharge. Is it a yeast infection.?

Could be. Typical symptoms of a yeast infection are a cottage-cheese like discharge and vaginal itching. If you think you might have a yeast infection, try an over the counter yeast medication. If your symptoms do not go away after using the medication, you might consider visiting the doctor.
It could be, but... Vaginal yeast infection typically is itchy with a whitish cottage cheese type of discharge. Being diabetic or being on oral antibiotics recently predisposes you to having one . If you are having other symptoms besides these, then have yourself checked by your doctor as this can be something else.