Those compound movements are definitely hard on your body, evenmore so if you do proper bracing your core, and holding your breath in like a can of unopened coke during the motion of deadlift/squats. But, it's very surprising when you've been training for 4 months and you're still having such a major issue with this? I mean don't get me wrong, i'm still worn out like hell after 5x8 of deadlifts/squats - but it's within limit.

Looking on top of whatever physical issues you may have, are you using too heavy of a weight? What's your height/weight/bodyfat ratio? You kept on increasing the weight during that 4 months duration?
Are you squatting more then your bodyweight for reps? Try 80-90% bodyweight for reps - those should be easy for a typical male.
Are you sure you have the proper form down? Proper form makes yourself feel "solid" - it's really a hard feeling to describe but it just feels right - and it took me 6months+ of solid form practice to get all my compound forms spot-on for my body's aspect ratios.

Also - are you consistent in that 4 months of weightlifting? ie. at the bare minimum, 3 type of compound lift(squat/bench/deadlift/ohp/row) every week for 16weeks without miss?
And no, i won't comment on your nutrition/other body related matters as it's not possible to comment on those with just words you've posted - i'm not a e-doctor.

Correct, to see any solid difference, at least 4-6 months of consistent effort must be done first! And if really things doesn't go your way - be very critical in evaluating your own effort or just get a personal trainer - as they will be accountable to evaluate every aspect towards hitting your goal (not those stupid p.trainers u see in gym who help ppl how to bench press only)

oh and.. 78-82 kg, that's fat for someone that short right? How's it feel to experience being skinny, and then fat, which is better?

i think you should put more focus/research about breathing during each lifts then. Im not expert enough to explain in detail because it's something i naturally learn what works best for me... but even myself don't hold my breath the whole duration incl unracking part - you'll feel pening that man, im sure alot of ppl can relate.

Also - don't worry about the # of kg's you're lifting, seriously in gym i can say noone cares if you're lifting an empty bar pun as long as you're not obviously fooling around hogging the spot. What's important is you MUST progress/increase your weights to actually see improvements/changes past the initial honeymoon stage of 1-4 months of muscle/physiological changes.

but if you just want to stay healthy, then it's not so important la... just keep practicing proper form, you'll know you have proper form by constantly leaving the gym without joint/bone/nerve pain, and only that sweet muscle soreness the next day.