The use of 'Prick' 'Pierce' etc

Hi

Could you please tell me if I understand the following words correcty?

Many thanks,

Tom

Some mistakes I think

3- A thorn is/has become embedded in my foot
4- A thorn got stuck in my foot

meanings…
1- and 2- are similiar
pricked means to just a small wound, maybe like a needle.
pierced means a bigger wound, but means more along the line of “cut”, so cut the skin and entered the flesh. i.e. a more major “injury”
3- and 4- have the same meaning I think but embedded implies that it has become lodged and is harder to get out.

the final two seem fine

Little do I know about many English words, I don’t think that “embed” is an apt word in the context. “Embed” is too formal.