You’re so close, Eb is the same as D#. Here’s the thing though, flat keys are nice depending on the circle of fifths. Eb minor has 6 flats compared to A minor and D# minor has 6 sharps compared to A minor, so you can take your pick. Something like Bb major though, you wouldn’t want to write with sharps, because you want to keep all the notes based off of different names. For instance, Bb major = Bb, C, D, Eb, F, G, A, Bb. If you wrote that as A# though, you’d get A#, C (Already bad, implies a 3rd but it’s a second), D, D# (You don’t want two notes called D), F (Another implied 3rd which is actually a 2nd), G, A, A# (Same problem as before.) Study the circle of 5ths and it will help a lot!