There are several different meanings for the word memory, which can lead to ambiguity. Two of these are
- the faculty by which the mind stores and remembers information:
I’ve a great memory for faces
the mind regarded as a store of things remembered:
he searched his memory frantically for an answer
- something remembered from the past:
one of my earliest memories is of sitting on his knee
When you say good memory, it is not clear as to whether you are referring to the effective quality of your recall faculty (meaning 1) or the affective quality of what is being recalled (meaning 2).
When you use the plural form, memories, the second meaning is clear since the first meaning is almost always singular.
If you wish to convey a high level of recall, I would suggest one of the following alternatives:
I have good recollection of my childhood.
I have a clear memory of my childhood.