Hola Shirley

Not quite - this verb is used as "ocurrírsele [a alguien]", where it's using the reflexive pronoun and also the indirect object pronouns - this is why you see both. They have different functions. 

Other examples where you can see it more clearly are:

Ayer se me ocurrió sorprender a mi novio con unas flores.

Yesterday I thought about surprising my boyfriend with some flowers.

Vigila bien a los niños, no se les vaya a ocurrir meterse en la piscina.

Watch the children, in case they think about getting in the pool.

The reflexive pronoun is always "se" here because the subject of the sentence is not the person, it's whatever the person "thinks of" (a bit like gustar), so it'll generally be conjugated in the 3rd person singular:

Comprar unas flores= subject

se ocurrió = verb conjugated in 3rd person singular, matching with the infinitive "comprar"

me (= a mí) = indirect object

It is as if we said: buying flowers came to my mind 

I hope this clarified it, it's a difficult one! : ))

Saludos

Inma