Why only three exercises and why did you settle on those three?
You're probably less than three months off of hitting your press and chin goals, so that's a good thing I guess.
A basic two day setup like this should work to get there. Depends a bit on when/how often you're training Muay Thai.
A) Weighted chin-up 4x2-4
B) Overhead press 4x8-10
C) Front squat 4x6-8
A) Overhead press 4x2-4
B) Chin-up 4x10-12
C) Trap bar deadlift 4x8-10
However, I'm not 100% comfortable sticking with such barebones training for so long. Simplified, uncomplicated routines are one thing, but there is such thing as being oversimplified to the point of neglecting movement patterns (not even an issue of bodyparts).
I'd work towards hitting your press and chin goal because it'll be fairly quick, and then drop those two exercises from your rotation for a while. Ditching them and working on similar movements will benefit your strength and musculature.
Does your gym have dumbbells? Dumbbell bench variations, even one-arm benching, could be an option. But there's nothing to be apprehensive about as long as you avoid failure (which you should be doing anyway).
Front squat, back squat, goblet squat, any lunge. Lots of options are good for athletes. On a related note, are you competing in Muay Thai or just studying recreationally?
See above. There have also been several programs written for martial artists, though guys in the Combat forum seem to like the 5/3/1 approach.
Many to consider, as mentioned above.