I advise you not to use 까먹다 in a formal context. It literally means peel (까다) and eat (먹다) something, as with a fruit or a wrapped candy. It was originally a joke (probably directed to children) in the sense of "how come you forgot it - did you end up eating it?", similar to "The dog ate my homework". Somehow it got popular and is used very widely. But it is certainly not for a serious occasion (it sounds frivolous and uneducated - some people frown upon it). In formal contexts, you should use the standard word 잊다(forget) or 잊어버리다("forget" with emphasis). "벌써 저를 잊은[잊어버린] 건 아니겠죠?". It can be used between friends too - "벌써 날 잊어버린 건 아니길 바라", "나(를) 잊으면 안 돼", etc. The difference is that it doesn't have that funny feel of 까먹다.