Fad diets are just that - fads. You can certainly live a low carb lifestyle, but all the "quick fix" diets will leave you disappointed in the end. Here's the basic 101:
Diet: there are a lot of methods to reaching the same goals, but a few "rules" that must be followed. Calories are the primary factor in determining fat loss. You must have a caloric deficit (burning more than you are eating) or you will not lose fat. Conversely, if you eat too little, your body will slow its metabolism and hang onto fat, so you have to find the right range for your body. Gerneral rule of thumb is 10-12x bodyweight in calories each day (higher in the range if you're working out). If you can, divide those calories into 5 or 6 small meals to eat throughout the day (every 2-3 hours). It will keep you from being hungry and keep metabolism up so that you will use the nutrients and burn fat more efficiently.
Once that is in order, check the content of your diet. You need to be getting enough protein to build and maintain lean muscle mass (which keeps metabolism high) which is generally .8 to 1g per pound of body weight.
Carbs should be complex. Avoid sugars and white foods when possible (white bread, white rice, pasta etc) because your body metabolizes them like it would sugar which increases likelihood of fat storage. Whole grain breads and brown rice and the like are burned more slowly and less likely to be stored. Vegetables are always a good choice, fruits are ok, but don't overdo it (sugar).
You must have fats. They are not the devil. But fat has 9 calories per gram (as opposed to 4 calories per gram for carbs and protein) so those calories can add up fast. A little healthy/unsaturated fat each day will help your body to use it's own fat for fuel (under a caloric deficit). As well as regulate hormones and various body functions.
Also good is to drink 1-3 litres of water a day.
Now, for a workout, 3x a week is a good place to start. You need to condition yourself some before going full force. If you want to go to the gym, a little resistance training hitting each muscle group will help get some muscle tone. If you decide to do it at home, a small set of dumbells or resistance bands will be okay. Cardio for 20-30 minutes 3x a week will help build cardiovascular endurance and burn calories. Please
don't feel self conscious about the gym. Everyone there is going in order to improve themselves, regardless of starting point (and most people in a gym are *not* in tip top shape - but working toward it.
) No one is judging you. Even if they were... who cares. You aren't there for them. It's all you, baby. Hope that's helpful.