In September, I left my hometown for university,and I left my daddy [“daddy” sounds childish; “dad” or “father” would be better] as well. Every time I called [call, not called; because you are talking about an ongoing thing, not about a specific past call] him and before l hang up,he never forgets to repeat a word. Call me more often. I don't know why at first,but I gradually realized that maybe he just want[s] to ensure my safety,to share my laughter and tears as our families usually do [did] in the past,or simply just want[s] to hear my voice. Susan, you can either write it in the present tense as shown above — if you want to emphasize that you are continuing to have these phone calls — or you can write it in the past tense like this: “Every time I called him and before I hung up, he never forgot to repeat a word: call me more often. I didn’t know why at first, but I gradually realized that maybe he just wanted to ensure my safety, to share my laughter and tears as our families usually did in the past, or simply wanted to hear my voice.” 我希望我能帮助你。

Add spaces after your commas. You've done well and added them correctly after the full stops, but you need to do the same with the commas.

I like your story. The meaning is quite clear. Here are some minor recommendations for your consideration: (1) "Every time I call him and before I hang up, he never forgets to say "Call me more often". (2) "I didn't know why at first, but I gradually realized that maybe he just wants to ensure my safety, to share my laughter and tears as our family has in the past, or simply just wants to hear my voice."