Can I honestly lose weight by just eating less/better?

I know many people promote this but I'm not 100% sure it's enough, at least for me.

I'm a 25M and I work an office job from 8:30 AM to 18:00 PM, with the bare minimum amount of physical movement involved. After work, I don't have time to dedicate myself to a sport or gym since I must go home to make dinner, clean the house or do chores in general. The only time I do some movement is on the weekend as I like going for long walks.

I'm 180cm tall and weight around 105kg, so I'm overweight if not straight up obese. I don't have any health problems since I do regular check-ups, but I'm not comfortable with my body for many reasons, mostly the fact that I can't wear many things I'd like to and I dislike looking at myself in the mirror when I'm naked.

After xmas holidays I've started a diet by cutting sugars almost entirely, eating more protein and vegetables and keeping an eye on the amount of carbos I eat. The only sugars I eat is for breakfast where I eat a cup of 0% yogurt with some cereals in it (corn flakes with bits of dark chocolate), as eating salty in the morning makes me sick (I'm italian and here we never eat salty for breakfast).

For lunch I either eat:

  • Salad with a can of no-oil tuna, 1 mozzarella, 2 slices of bread and some walnuts.
  • Rice with chicken, carrots and zucchini.
  • Pasta with tuna, carrots and zucchini.

After lunch I often also eat 1 square of 100% chocolate, which helps me keep my sweet tooth at bay.

For dinner I have not an usual plate but it often consists in some type of piece of meat and vegetables with bread.

I almost never eat snacks between meals, and I keep count of my calories by staying under 1600 kcals a day everyday.

After a month and a half there has been no changes, my weight is still the same (weighted myself right after waking up this morning without having eaten any carbs the previous day, so no water retention) and my body fat is also still visually the same. I honestly don't know what more can I do. Am I doing something wrong?