I don’t currently drink protein shakes.. I think I should start including them after work before I go to the gym.
On a typical day I skip breakfast, then eat lunch at 12, and then I don’t eat again until after the gym around 8. So I think a protein shake around 6 when I get off from work would be helpful
If you're getting newbie gains, I recommend getting extra protein from post-workout shakes, and maybe pre- also. Sounds like this is the right time, when your body is adapting. Some whey protein, 20-25 grams, within 30 minutes after working out will intensify your muscle protein synthesis periods. Right after working out is when your muscles are damaged and need the nutrients to start making repairs (synthesis).
You don't really need more than 20-25 g of protein per sitting. The body does not intake more than that at one time. Since you're at two meals per day, another helping of protein will help. Personally, I think 8 hours between meals is long and you could graze on something like nuts or have a yogurt between 12 and 8.
Also you don't need to have the extra protein on non-workout days. But you might need the extra protein on non-workout days in the beginning, when you're having initial gains. After that initial gain period, your body has adapted and the extra protein on non-workout days, when you're not moving, just means extra calories and fat gain. Add the protein within 30 minutes of working out and within 24 hours of the workout. Beyond that, your body is for the most part through with recovery and really doesn't require the extra protein.
At least it works for me in my case.
If you want to lose weight, which sounds like the priority, you need a caloric deficit. That's a must. Restricting to two meals a day is probably helping. Exercise takes away less calories than you think. The best way to reduce calories is to eat less. Eat less but eat stuff that gives you your required macros.