with regards to the other user's comment, they are not wrong in that there are medications that can cause tissue necrosis, and this being the circulatory system that can include the heart.

but in re estradiol specifically (and steroids in general), we tried looking but weren't able to reach any meaningful conclusion about any tissue necrosis.

there doesn't look to be much literature surrounding this topic, at least that we could find anyways. there is this review, which provides examples of medications that while causing pain and discomfort when accidentally injected into a vessel otherwise did not result in considerable complications. there are of course other cases with other medications that went far worse, but notably there didn't look to be any steroidal medications among them. the only thing we can really conclude is that tissue necrosis in the heart is not a given. but this doesn't mean it's out of the question entirely either.

this tutorial about accidental intra-arterial injections states:

Whilst the exact pathophysiology is unclear (and likely varies by drug) thrombosis is believed to represent a final common pathway. This may then lead to tissue ischaemia and necrosis.

the whole thing appears to be a very broad generalization, one that surrounds a) some medications often used in hospitals and what to do if a medic mistakenly injects something into a vessel, and b) illicit drug use. but again, there is nothing in specific about estradiol or any steroids.

otherwise the most specific stuff we could find were anecdotes from online forums, which frequently mentioned elevated heartrate, it feeling awful in general, but often not being problematic beyond that. most of these accounts were about testosterone, which is a different drug, but it is also a steroid; the number of molecules injected was also more numerous than you would ever do in pretty much all of those internet posts we read.

there isn't a satisfying answer—there is only a considerable lack of information. with what little is out there though, we'd guess that you won't die and that you might be just fine given some time and caution, albeit getting checked out by a medical professional is still a good idea. well either that or more likely from your description you just punctured a vessel of some kind.

stay safe, stay comfy, and keep calm!