Hello.
Thank you for your query at DoctorSpring.com.
I understand your concern.
As you suspect, your acne and excess facial hair (mild hirsutism) are most likely due to hormonal imbalance, possibly excess androgens. You need further evaluation for this.
A common cause of irregular cycles and hirsutism is PolyCystic Ovarian Syndrome (PCOS) which affects young females. Obesity is a risk factor for this. This is a benign condition which responds well to treatment.
In your case, if you have been sexually active, then you first need to rule out pregnancy. You can do this by taking a urine pregnancy test now, because it has already been a week since your expected period.
If it is negative, wait for another week for menstruation to occur. If after a week, you still do not get a period, then you can take a course of Medroxyprogesterone 10mg tablets, twice a day for 5 days. After stopping this course, menstruation will occur.
Once you get your period, you need to test levels of Serum Testosterone, Prolactin, LH and FSH on day 2 of your next cycle.
You also need to get an ultrasound of the pelvis to have a look at the ovaries.
You can get these tests done and upload the results for further management. Alternatively you can consult a gynaecologist for the same.
Let me know if I can assist you any further.
Thank you.

Hello.
Delayed periods can be due to Lamictal, especially if you have only recently started it. Changes due to the drugs, stress, etc may also lead to a delayed period. Since you also have features of excess androgens, we need to evaluate for these causes such as PCOS.
An estrogen-progestin contraceptive as first-line pharmacologic therapy for most women with PCOS.
I hope this answers your questions.
Let me know if you have additional queries.
Thank you.