I was thinking of making competetive teams, but is it worth it if I will only ever use them In-game?
If you are not planning on competitive battling, there is no use other than doing it for fun. Competitive teams are geared towards a different environment than play-through teams, so certain moves and roles common in competitive battling are a waste of a slot in-game (i.e. defensive and support Pokemon and moves). It's up to you if it's worth it.
It's a strange question because if you want to buil a competitive team, do it. Questioning if it is worth or not it's useless. You can partecipate events like tournaments or just battle your friends. And a off-topic answer: if your internet is so bad try to go near your router or turn off some devices connected to the internet if you can then try and battle online.