She was fasting to make up missed days, but she said: I am fasting six days of Shawwaal
Question

When I was younger I was very shy. One day when I was fasting what I owed of Ramadan, my father– may Allah have mercy on him – asked me, Why are you fasting? Out of shyness, I told him a lie and said that I was fasting sawm as-saabireen (the fast of the patient, i.e., six days of Shawwaal). I was thirteen or fourteen years old – and Allah knows best – and I have continued to fast the six days of Shawwaal until today. When I grew up, I started to wonder: was I fasting what I owed or the six days? Please note that when I grew up, I began to fast the six days and what I owed, but now I have made a schedule for myself:
The number of years since I reached puberty is nineteen. The days that I did not fast are seven days, but I made it five days because I used to fast – and now I am applying this schedule, and I am still doing that – I fast from Sunday until Thursday, and give zakaah for each day – and Allah is Oft-Forgiving, Most Merciful. Because of shyness, which is deeply entrenched in me, I fasted the fast of the patient, which is six days.
Have I done anything wrong before Allah, because I told my father that I was fasting the days of the patient and I did not say that it was what I owed from Ramadan?
Praise be to Allah.Undoubtedly shyness is one of the greatest of good characteristics, especially in a woman, and especially if she is a young girl at this age.
If your shyness prevented you from speaking frankly about fasting to make up the days that you missed in Ramadan because of your menses, you could have used some kind of double entendre or vague words. So you could have said for example, “I am fasting like everyone else in Shawwaal,” or “Fasting is prescribed in Ramadan and at other times,” and the like. 
Your saying, “I am fasting the fast of the patient,”may carry a sound meaning, because this is how fasting is: it is the deed of the patient and fasting is a deed that requires patience, so it was not necessarily a pure lie, but that is on condition that when you said it you had this sound meaning in mind. 
Whatever the case, we hope that what you said may be forgiven and overlooked by Allah, because you were overwhelmed by shyness that distracted you and made you unable to think of what to say or to come up with appropriate words. 
For more information, please see fatwa no. 27261 about the ruling on using double entendres. 
Secondly: 
Fasting depends on the intention, not what the fasting person says unintentionally. If you intended to make up missed fasts, then it will be counted according to your intention, and this fast is valid and is sufficient to make up what you missed during your menses, even if you told your father that your fast was naafil or something else. None of that has any impact on the ruling on your fast, because the Prophet (blessings and peace of Allah be upon him) said: “Actions are but by intentions, and each person will have but that which he intended.” Narrated by al-Bukhaari (1) and Muslim (1907). 
For more information, please see fatwa no. 109351 
Based on that, you do not have to make up these days, or to put yourself through the hardship of the schedule that you mentioned. Rather what is prescribed in your case is to offer whatever naafil fasts you can, without burdening yourself with something that it is not proven that you have to do in the first place. 
And Allah knows best.