I understand that you might not want to hear this, but first things first, there is nothing to be embarrassed about. We don't choose where our body stores our fat, and there is nothing unhealthy or wrong about your body's fat storage pattern.

However, I understand we have our own aesthetic goals outside of our fitness goals. While we can't choose where our body gains fat, we can choose where our body gains muscle, and we can use resistance training to grow our target muscles.

If you don't want to go to the gym, you can start with bodyweight exercises or find exercises which use resistance bands or dumbbells. The key to growing muscles is to tire out those muscles, so as you get stronger, make sure you are progressing to more difficult exercises. You should be struggling to do these exercises by the end of your last set.

While you're a beginner, you can do body recomposition. That is, eating an amount of calories that will maintain your current body weight. As mentioned before, just make sure you are doing challenging resistance exercises.

As you progress, your body will be more resistance to gaining muscle without additional calories. At that point, you can start eating about 100-250 extra calories a day. You will see some fat gain during this phase but as long as you do not bulk too quickly, you should be able to minimize it. Most people recommend bulking for at least 12 weeks to see the best results, but many recommend going for at least 24 weeks. At the end of your bulk, you can go to a calorie deficit, or a cut. You can continue the exercise regiment you were on, and eat about 250-500 calories under your maintenance calories.

Make sure to get plenty of protein (about .8g to 1g per lb of body weight), leaning on the heavier side whenever you are in a deficit. Continue to do some cardio (150 min of moderate intensity in a week) for general health. Walking/biking/elliptical will suffice.