Welcome to the forums Dejackson, we are about the same place with our squats and deads.
About your press, you really need to reset and then use microplates (1 lb - 2.5 lb). Your typical press progression may be 115 -> 117.5 - >120 ->122.5 ->125 ->127.5 etc. I was running into a brick wall with the press, each rep was Herculean, but it wasn't until I went to micro loading that I got steady progress up to and beyond my sticking point. I put up 152.5 yesterday this way, and if I hadn't hurt my shoulder outside of the gym, was feeling strong enough to get all the sets.
I introduced chin-ups very early because I like them and I wanted a stronger shoulder (I have some old injuries). The typical SS plan prescribes deads/cleans and then deads/chins/cleans/chins/deads etc. in the advanced novice program. I personally enjoy deadlifting every week, but I have had a much better time recovering by following the advanced novice template.
Good luck and great gains!