She bled after having an injection for temporary contraception; what should she do?

Praise be to Allah.

Firstly: 

It is permissible for a woman to use means of contraception on a temporary basis, to safeguard her health if she is unable to bear pregnancy. 

Shaykh Ibn Baaz (may Allah have mercy on him) said: 

It is permissible to use temporary methods of contraception for legitimate shar‘i reasons. End quote. 

Majmoo‘ Fataawa Ibn Baaz, 9/434 

Shaykh Saalih al-Fawzaan said: 

If this spacing or delay of pregnancy is for health reasons affecting the woman, such as if she cannot bear pregnancy and childbirth due to some special reason or circumstances, such as sickness, then there is no reason why she should not be given something that will prevent pregnancy occurring until the situation that makes it too hard for her to get pregnant and give birth changes. End quote. 

Al-Muntaqa min Fataawa al-Fawzaan, 89/20 

Secondly: 

This woman is mustahaadah (experiencing abnormal bleeding). If her previous menstrual cycle is known, then she should refrain from fasting and praying during the days of her usual period, then when that time ends she should do ghusl and resume fasting and praying. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about a woman who bleeds a lot; how should she pray and when should she fast? 

He replied: 

In a case such as this, when a woman bleeds a lot, the ruling is that she should stop praying and fasting during the days of her period according to her previous cycle before this problem affected her. If her period used to come at the beginning of every month for six days, for example, then she should stop praying and fasting for six days at the beginning of every month; when that time ends she should do ghusl and start to pray and fast again. 

How this woman and others like her should pray is as follows: 

She should wash her private part thoroughly and put a pad or sanitary towel, then do wudoo’. She should do that when the time for each obligatory prayer begins; she should not do that before the time begins, rather she should do it after the time begins, then pray. She should also do that if she wants to offer naafil prayers at times other than the obligatory prayers. In that case, so as to avoid hardship, it is permissible for her to put Zuhr together with ‘Asr, and Maghrib with ‘Isha’, at the time of the earlier or later prayer, so that she only has to do this once for two prayers in the case of Zuhr and ‘Asr, then Maghrib and ‘Isha’, and for Fajr. So instead of doing it five times a day, she only has to do it three times. End quote. 

Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 11/220 

Thirdly: 

You said that she used to pray and fast during the time when she was bleeding. The prayers offered during the time of her usual period are not valid, but she does not have to make them up, because a woman who menstruates does not have to make up prayers. 

With regard to fasting, it is not valid during the days of the menstrual period and she has to make them up. She has made up sixteen days; if these were the days of her period or more, then she has done what is required of her and she does not have to do anything more than that. But if the days of her period were longer than that, she should make up what still remains.  

And Allah knows best.