Personally
Myself
pronoun
I am talking about my self, my own body… In other words, this is about me personally or what I myself have done.
私自身 literally means "I myself," and it's used to emphasize your personal involvement in something. For example, you may say 私自身の考え to highlight that something is your own thought, or 私自身から言う, to really stress that you'll personally be the one to say something to someone, without going through any intermediaries.
The readings are a bit weird here. The 私 is わたし, but the 自 and 身 use the readings you learned with the kanji. Just imagine the 私 saying to the other two, "I myself will use my vocab reading, but you two should use your kanji readings — got it?"
私自身びっくりしている
I am surprised myself
私自身分からない
I don't know myself
私自身ふしぎだ
I wonder myself
私自身はコーヒーもお茶も両方のみます。
Personally I drink both coffee and tea.
私自身で魚を切ったことはありません。
I have never cut fish myself.
私自身は考古学を学びたいという思いが強いですが、他の人にはあまり分かってもらえません。
I personally have a strong desire to learn archeology, but others don't understand me.