both are correct – androgen dominance can lead to estrogen dominance. When testosterone is high in a woman (usually higher insulin is at play here), this will cause annovulation (no ovulation). When she doesn’t ovulate, progesterone doesn’t get produced, therefore during her luteal phase when progesterone should be highest, it’s not, which leads a higher estrogen to progesterone ratio (i.e. estrogen dominance) in that part of her cycle. Makes sense?

I have some one dealing with PCOS, she started take the birth
control pill. I would like to give her more info please?

 PCOS (Polycystic Ovarian Syndrome) affects a reported ~10% of women, but that’s a low estimate in my opinion. The estrogen dominance (and often excess androgens) present in these women will lead to many states of dis-ease downstream. 
These women may struggle with a wide variety of symptoms including weight gain, fatigue, facial or excess body hair growth, thinning hair on the head, infertility, acne, irritability, insomnia, and headaches.
As usual, we want to focus on understanding the dynamics at play in this type of imbalance (and not the diagnosis).  Many women with PCOS are not ovulating optimally (or, therefore, not making much progesterone) and this puts them in an estrogen dominant state.  This anovulation is often caused by excessive testosterone as a result of high insulin levels from insulin resistance.  Checking her blood sugar levels including fasting insulin is good idea.
We know that insulin resistance is epidemic – hence why I created a whole course on the subject! And it is indeed reversible in many cases with persistent lifestyle change and targeted short-term supplementation to increase insulin sensitivity.

In the case of PCOS, I want to introduce you to the power of inositol.

Inositol has been shown repeatedly to restore ovulation (and here) and increase pregnancy in women with PCOS, in both normal weight and obese categories.   In many of the high-dose studies (and here and here and here,  from 1200-4000mg daily), there was a marked improvement in glucose, insulin, and testosterone levels as well, showing the nutrient is addressing the common metabolic and interactive hormones drivers of PCOS.   There were ovulatory benefits in lower-dose studies (e.g. 200-400mg/day)  but less or no other marked improvement in other metabolic markers (e.g. insulin). One study also identified dramatic improvements in two common symptoms of androgen dominance (acne and hirsutism)  in young women with PCOS.  Duration of treatment in the studies ranged from 3-12 months with significant benefits being demonstrated (where measured) by the three-month mark.  I typically recommend 2500-3000mg/day for my own clients.
Both myo-  and  d-chiro inositol  forms have been shown in most studies to be effective at reducing insulin resistance.  A couple of studies have looked at this opportunity more closely and identified  more rapid benefits achieved using a synergistic combination of myo- and d-chiro-inositol as opposed to myo-inositol alone.  Improvement in the end was equal in extent for the two scenarios; the combination was simply effective more quickly.   There is some evidence that a lack of availability or utilization of d-chiro inositol in tissues is a direct causative factor in insulin resistance.   Whether this is a primary or secondary effect is unclear.
Supplement options are readily available.  A combination myo- and d-chiro inositol product can be found in items such as Designs for Health’s “Sensitol” (capsules).   Pure Encapsulations offers the myo- form in “Inositol” which is a loose powder (a nice, easy option given inositol is sweet and quite palatable).   When using inositol separately in some way, I recommend doing so in combination with a broad-spectrum B-complex supplement to ensure availability of key cofactors.
High-dose inositol is contraindicated (as is true for the vast majority of supplements) in those with kidney disease.  Otherwise, none of the studies I reviewed identified any significant side effects or safety concerns after over a year of intake up to 4 grams daily.
Research into the use of inositol to counter depression or anxiety has used much higher doses (6-18g/day).  For example, a dose of 18g/day was found to be as effective as fluvoxamine (an SSRI) after a month of use in treating panic disorder. 

Please note that the birth control pill is often given as a band-aid solution, and will lead to further consequences since it depletes B vitamins over time, and causes wear and tear on the gut lining. And not to mention, can increase estrogen states in the body, which can impact thyroid function and a whole host of metabolic consequences downstream as a result. 
Hope this helps give you some direction and information to share with her. Please let her know we can help her if she needs the support.