Don't worry about it.
It is a good reason to stick to basic vocabulary, the simple words you learn in English courses.
The list of words and expressions that might have a sexual connotation is endless. It can be a kind of game for teenagers to tease and embarrass each other by pointing out possible sexual meanings in innocently-meant words.
But everything depends on context and tone of voice and body language. If you don't mean it in a sexual way, nobody will think you mean it in a sexual way. Take what your friend said as a friendly tip, and change to saying "dad" or simply "my father," but don't worry about it.
Suppose a native speaker, a woman, said: "My daddy always used to say that being brave isn't not being scared, being brave is being scared and doing it anyway." I would interpret "daddy" to mean "her father" and I would never even think of any sexual connotation.
There is a famous song in which a woman is using "daddy" with a sexual connotation: <a href="https://www.youtube.com/watch?v=6UdEKsTWNFs" style="color: rgb(17, 85, 204); font-family: Arial, Helvetica, sans-serif; background-color: rgb(255, 255, 255);">Mary Martin: My Heart Belongs to Daddy</a>. But how do we know the connotation? It is not because she uses the word "daddy," it's because of the way she uses it. She makes it clear when she says "I've come to care/For a sweet millionaire." The whole point of the song is that she now rejects other boyfriends because "my heart belongs to Daddy." So we know that "Daddy" is not really her father, "Daddy" is an old, rich boyfriend.
Your dictionary should explain. If not, you need a better dictionary.
New American Oxford Dictionary
sugar daddy | ˈʃʊɡər ˌdædi | noun informal a rich older man who lavishes gifts on a young woman in return for her company or sexual favors.
Words and phrases which have sexual connotations (or double meanings) in English are called inuendos. There are way too many to list, but you can find a lot of "Inuendo bingo" videos on Youtube which basically derive their humor from these expressions.
Generally inuendos aren't bad, especially if you don't make them on purpose.
As for bad words in general, just try to stay away from any offensive language, and even if you do make a faux pas most people will not hold it against you.
All in all, don't sweat it too much, even when you do make these types of mistakes, they tend to become fun inside jokes, rather than actual problems.
Hope this helps! If you still have any questions, feel free to ask.
Did she mean sugar daddy? Here's the meaning of it. Sugar daddy is a slang term for a man who offers support (typically financial and material) to a younger companion, e.g. a kept woman. According to the urban dictionary: A sugar daddy is a man who provides money or other favors in exchange for sexual relations ( you can check on this link <a href="https://www.quora.com/What-is-a-sugar-daddy" style="background-color: rgb(255, 255, 255);">https://www.quora.com/What-is-a-sugar-daddy</a>)
You might also want to avoid the term "cougar" that addressed to a particular woman. A cougar is typically defined as an older woman who is primarily attracted to and may have a sexual relationship with significantly younger men. (<a href="https://www.thoughtco.com/what-is-a-cougar-3534236" style="background-color: rgb(255, 255, 255);">https://www.thoughtco.com/what-is-a-cougar-3534236</a>)
Hope they help.