I'm really sorry, but me and my friend won't be able to make it today.
文脈が分かりませんが、パーティーなら I'm really sorry, but me and my friend won't be able to make it to the party today. や I'm really sorry, but me and my friend won't be able to attend the party today.
イベントなら I'm really sorry, but me and my friend won't be able to make it to the event や take part in the event today.
Me and my friend はカジュアルで話す時によく使います。正しい文法は My friend and I です。
Example:
I'm really sorry, but both my friend and I won't be able to ... (join, make it, come, attend etc...)シチュエーションによって動詞が変わります。
「友達も」ですからパーティーだと勝手に思っていますが、パーティーなら I'm really sorry, but both my friend and I won't be able to come to the party/attend the party/make it to the party todayがいいと思います。