I suppose there could be two different meanings on this expression. ① It could be used when it was required to emphasis on the subject. 私ときたら、　＝＞　Regarding myself, There is actually no exact translation for "～ときたら" in English. But if I have to translate, I would do it into something like examples below. <example> 彼女は一日中勉強しっぱなしです。 She has been keep studying whole day. ＞彼女ときたら、一日中勉強しっぱなしです。 Regarding her, she's been studying whole day. About her, she's been studying whole day. ②～と来たら（～ときたら）　come with ～ 私ときたら　＝＞　why don't you come with me. -- NOTE: Since the question sentence has been written with only Hiragana (without Kanji), It is high possibility that the questioner's sentence had been quoted from a sentence type of example sentence①.

That's nonsense. "Watashi to kitara" means "if you come with me"

と来たら (( ときたら )) means: when it comes to ...; concerning; where ... are concerned