Is the word machuquei the same in Brazilian and European Portuguese?

No

While the spelling and fundamental meaning of "machuquei" are identical in both dialects, the answer is No because there are significant differences in grammar and typical usage.

1. Grammar (Syntax): In Brazilian Portuguese, it is natural and common to place the reflexive pronoun me before the verb (proclisis), such as "me machuquei." In Continental Portuguese, the pronoun typically follows the verb (enclisis), such as "machuquei-me."
2. Usage (Vocabulary): While "machucar" is used in both, Portuguese speakers in Portugal more frequently use the verb "ferir" (to wound/injure) or the expression "dar uma contusão" (to get a bruise/contusion) for more significant injuries. In Brazil, "machucar" is the standard, go-to word for almost any physical injury, regardless of severity.

Brazilian Portuguese (Natural Usage)

1. Eu me machuquei todo na queda. (I hurt myself all over in the fall.)
2. Me machuquei o pé jogando bola. (I hurt my foot playing ball.)
3. Cuidado para não se machucar! (Be careful not to get hurt!)
4. Eu me machuquei muito no acidente. (I hurt myself a lot in the accident.)
5. Ela se machucou com o ferro de passar. (She hurt herself with the iron.)

Continental Portuguese (Natural Usage)

1. Eu machuquei-me a perna a jogar futebol. (I hurt my leg playing soccer.)
2. Feriu-me o braço com a porta. (I hurt my arm with the door.)
3. Machuquei-me o dedo a cozinhar. (I hurt my finger while cooking.)
4. Fiquei com uma contusão no joelho. (I got a bruise on my knee.)
5. Ele feriu-se durante o treino. (He injured himself during training.)