Wa alaykum Asalaam Sister,

First, welcome to Islam! I myself also converted to Islam during Ramadan, and I remember that sweetness and the fierceness of those days. Everything is so new, so hard, but so beautiful! I can also relate because I missed several years worth of Ramadans because of persistent pregnancy and nursing for 6+ years.

Regarding making up fasts you’ve missed because of having your period, there is a consensus among the scholars that yes, we must make up these missed fasts before the following Ramadan.

This comes from an authentic hadith wherein ‘A’ishah (may Allah be pleased with her) said:

I used to have fasts that I still owed from Ramadan, and I could not make them up until Sha`ban (the moth after Ramadan), and that was because of the position of Allah’s Messenger (peace and blessings be upon him) [as a husband]. (Al-Bukhari)

Ibn Hajar said:

It may be understood from her keenness to fast them in Sha`ban that it is not permissible to delay making up fasts until the next Ramadan begins.

So, yes, technically, women should make up those fasts before the next Ramadan arrives. However, Allah does not hold us accountable for things we do not know. Since you are a new Muslim, you can only do what you are aware of. And Allah knows what is in your heart.

So, do your best this year with this new knowledge you have, to make up those fasts missed from the past two Ramadans before the next Ramadan, insha Allah.

I hope this helps. Please keep in touch. 

Salam.