Weight loss and fat loss...the reason it happens no matter what "diet" you choose is due to being in a calorie deficit. Meaning you burn more calories than you take in. No all these calories aren't burned by endless exercise.
Unless you have a legit food intolerance avoiding gluten, dairy, bread is not the reason you will ultimately lose weight.
If certain types of foods are trigger foods for you though, you may find it is easier to avoid those and opt for others and in that case your alternatives may also be lower calorie or not as bingeworthy which also contributes to my point...you need a caloric deficit.
If you're on a super low cal 'diet' and not making progress then for sure visit one of the macro calculators below to get an idea of what you SHOULD be eating (calorie wise --- these aren't meal plan - but you may find some great recipes).
Diets should have a definitive start and finish. You need to have a maintenance plan in mind...so that after you see results you don't gain the weight or inches back.
Exercise is not a must but I find it to be a good solid addition. Be more active in general and you can do ok with just nutrition tweaks. HOWEVER, if you want to really change how your body looks and not just lose pounds then resistance training (not endless treadmilling) is needed and there are multiple methods you don't have to specifically go to a gym.
Macros, Inc macrosinc.net/services/macro-calculator is a GREAT resource for getting your estimated calories and macro breakdown needed for your goals (Fats, Carbohydrates and Protein). Their Facebook group is one of my favorites. There are no bad foods...just bad eating plans. They give away A LOT of information for free and the members in there are also helpful.
IIFYM.com is also a good macro estimator.
You need to try the macros counts for a few weeks and see how you do, track what you eat and make changes as you see results. So if you're current plan is failing make sure you're also tracking and being honest with yourself...weighing food is actually very helpful. Weighing isn't needed forever but will help you better understand what is in your perceived 'servings'.
Using a macro approach vs a "special or faddy diet" approach helps you eat what you like as you make changes. 80% mostly great food choices will allow you 20% less optimal ones...like my favorites oreos, ice cream, red wine and curls of cheese.
Protein shakes are great...but if your plan requires 2-3 a day til infinity then there's a better way not only for your results but your wallet so please keep an open mind!!!
Anywho....diets aren't meant to last but your results should...make it maintainable. Questions? Let me know :)