Hormones influence some of the most basic functions in the body, including your "internal thermostat" and metabolism, so it's not too surprising you are getting what feel like strange side effects such as shivering. Chills are a known side effect of estradiol and other hormone treatments but it shouldn't be a dangerous one.
The leg cramps could be caused by both the EE and/or the MCT, but (this is where my experience ends) there are many people who say it's more a matter of your technique when administering. If you haven't looked into proper technique, there are videos on YouTube that could help. I've also heard that subcutaneous injections are less painful for some people.
I saw you told your parents the other day too I think?
Congrats, I hope things continue to go well!