Usually when you use fui=ir, an "a" will always come after the verb, whereas fui=ser will not have the "a".
Susanna, past participles should agree in gender and number with the word they modify. I believe "Fui seguido" would be correct if the person being followed is male or of otherwise unknown gender, and "Fui seguida" if known to be female. Since we don't know who the "I" is who is making the statement, you can infer from the -a that it is a female.
Me fui enseguida (en seguida seems to be accepted too) is more I left shortly (after sth) or I stayed little. e.g: I went to the bar, but stayed little because none of the lads was there. Fui al bar, pero me fui enseguida porque ninguno de los muchachos estaba allí.
Enseguida is used to give the idea of a short amount of time
Don't use permanent vs. temporary as the way to choose between ser and estar - it creates too many questions. Estar is used for location and condition, plus certain set phrases, and ser is used for most everything else. In this case, this is the passive voice. "I was followed..." and then the rest of the sentence would be something like "...by the masked man." In Spanish, ser is always used for the passive voice.