Egoism, altruism, and altruistic egoism

So I was thinking about this today. How much different is egoism from altruism? It's not like an egoist will ignore others. Is helping others beneficial to the self? I would say yes. I'm not so sure about this, as I only speak of my own experience. I enjoy helping others. And I do it from an egoist standpoint. I help others and feel good about it. And I help others to feel good about it. If I believed my efforts were fruitless, I doubt it would be as enjoyable. I think it is safe to say (at least for me) that when I cannot explain something to someone, it is very painful inside. Like last night (it was after 9:00pm or so), I went walking with my mother. She looked at the moon and asked me
if the bright star next to it was Venus. So I thought it would be an opportunity for me to explain to her the concept of an inferior planet and why Venus can only be seen at sunrise and sunset. So I first asked her where Venus is in the Solar System. She looks at her fingers, and counts to two. Yes, Venus is the 2nd planet mom. And what is the third planet? Earth. Ok, and where is the moon? It goes around Earth. So then I asked her how it would be possible to see Venus at nighttime, when we are facing away from the sun. She didn't understand what I meant. I felt so bad. I tried to explain to her how Venus is an inferior planet and how it cannot possibly be seen at nighttime, like Mars. I asked her to imagine the orbits of Earth and Venus, and find out where they could be positioned in such a way as to be seen at night. But by this time we had already reached home and I ran out of time to explain. I felt so bad. Oh well. Bye mom, goodnight.