Praise be to Allaah.  

Firstly: 

When a woman does not fast because of her period, she has to make up the days that she missed, because ‘Aa’ishah (may Allaah be pleased with her) said: “That – meaning menstruation – used to happen to us and we were told to make up the fasts but we were not told to make up the prayers.” Narrated by Muslim, 335. 

Secondly: 

We have already stated in the answer to question no. 26865 that it is obligatory to make up days missed in Ramadaan before the next Ramadaan comes; it is not permissible to delay it except for those who have a reason. 

Thirdly: 

Whoever is obliged to make up missed fasts but then is unable to do so because of sickness or weakness for which there is no hope of a cure should feed the poor instead, one poor person for each day.

 Shaykh Ibn ‘Uthaymeen was asked in Fataawa Arkaan al-Islam (p. 455): 

A young girl got her period and she fasted the days of her period out of ignorance. What does she have to do? 

He replied: 

She has to make up the days that she fasted during her period, because fasts observed whilst menstruating are not accepted and are not valid, even if she was ignorant of that, and there is no limit to the time when they can be made up. 

Here is a case which involves the opposite scenario: A woman started her periods when she was young, and she was too shy to tell her family, and she did not fast Ramadaan. This woman has to make up the month that she did not fast, because once a woman starts her periods she becomes mukallifah (accountable for her deeds), because menstruation is one of the signs of having reached adolescence.  

He was also asked about a woman who did not make up the days from her period in Ramadaan until she owed nearly two hundred days, and now she is sick and old and cannot fast – what should she do? 

He replied: 

If this woman will be harmed by fasting as mentioned in the question, because she is elderly and sick, then she should feed one poor person for each day. She should calculate how many days she owes from the past and feed one poor person for each day. 

Fataawa al-Siyaam, p. 121. 

For information on how much must be given when feeding the poor, see question no. 38867. 

In conclusion: 

If you are able to fast then you have to make up the days. If you will not be able to fast then you have to feed one poor person for each day. Try to figure out how many days you did not fast until you think it most likely that you have reached the right number.