That's right. You now have all the birthdays. Let's count them, shall we?
Your physical date of birth according to the secular calendar
Your physical date of birth according to the Hebrew calendar
The English date of your conversion
The Hebrew date of your conversion
Rinse and repeat for any other conversions or geirut l'chumrah
Half-birthdays for all of the above, as according to your minhag
It is your choice whether to count the dates of prior conversions or not. Some would be adamant that you should not give any validity to a non-orthodox conversion (and you probably shouldn't advertise the fact). However, in my opinion, whether you view it as a halachic event or not, it was (hopefully) still a monumental day in your life and on your road to being an orthodox Jew.
In practice, you'll probably fall into some kind of celebration cycle. For instance, I always remember the day of my conservative conversion because it is Zayin Adar (7 Adar), the day of Moshe Rabbeinu's death. I don't remember the English date. However, it's the opposite with my orthodox conversion. I can only remember the English date and not the Hebrew. But I don't celebrate any of them, including the dates of my physical birth. I'm just not a "birthday" person.
However, I do celebrate Shabbos Chanukah each year because that is when I learned my orthodox conversion had been approved, and I just had to wait for all the rabbis to be back in town. That is the day I felt such relief and gratitude and like darkness had really turned to light (apropos, no?).
You can celebrate as many (or as few) of these dates as you wish. They are all your "birthday." If you need to find the Hebrew date, check out the Chabad website's Birthday Calculator.
Now, how do you celebrate a Jewish birthday? Beats me. To my knowledge, there is no answer. As my first rabbi told me, "I don't know. Go buy a lottery ticket." #Truth.