"Sometimes I'm scared of myself."
Translation:לפעמים אני מפחד מעצמי.
Yes. But there are some situations that one of them wouldn't be used. For example, the infinitive לפחד (lefachéd) is used, rather than לפחוד (lifchód), as well as the past form פחד (pachád) rather than פיחד (pichéd).
Can you give examples in a sentence for each situation? Telling me they are pa'al and pi'el respectively, I already know that, I am asking why I got it wrong when I used פוחד if the definition is correct and the answer is calling for the pi'el verb instead.
You didn't get it wrong.
As Amir said, to sound OK in Modern Hebrew it's advisable to use only pa'al for past tense and only pi'el for the infinitive; and you can use either for present and future.
Grammatically you can use both for any of the tenses.
What I'm about to write probably will be more confusing, but I think the word that fits here the most is מפוחד. I don't know how to explain it properly, but "מפחד מעצמי" is more like "I'm scared of myself at the moment", while "מפוחד מעצמי" hints that the person is scared of all sorts of things he could\can do, and unnecessarily at the moment (and most likely not at that moment, but rather things to happen).