I am involved in sports, I play soccer, and I am a goalkeeper. A month ago, during a match, I felt a sharp pain in the lower part of my abdomen. In one reaction, I felt a sharp pain, and after a few days, it moved to the adductor. I went to various doctors, and they told me that it appeared from the lower back because I have a slight displacement but that surgery is not needed, just strengthening that lower back part. And what happened on the abdominal wall that caused me pain is not a hernia, just a strain, and it moved to the adductor!
Now I am undergoing therapy with electricity, magnet, ultrasound… for the abdominal wall and adductor! They told me not to do any exercises and strengthening, to calm down, and that these therapies will help me. Can I do exercises for my back, lower abdomen, and adductor along with these therapies? Is swimming good for me?

Muscle injuries require relative rest during the initial healing phase. Namely, muscle tissue is soft, and even minor tension or contraction can increase the injury by increasing tension. Furthermore, it should be noted that reducing pain is not a sign of sufficient muscle healing, which is the main cause of recurrent muscle ruptures. Especially in soccer players, particularly in the groin area and abdominal wall.
Although there is disagreement in the field about how long it takes for a muscle to heal, and follow-up ultrasound examination is more of a guidance in this process rather than an objective sign guaranteeing visible completion of healing, the advice of doctors and physiotherapists on when it is good to continue and with what physical activity after muscle strain is a matter of personal experience.
In Scipion, we follow a protocol where rest is important for the first three weeks after the injury. Then, if the symptoms have disappeared, we continue with a gradual return to full training load.
In your case, back exercises necessarily involve a strong contraction of the abdominal muscles, so they are not recommended in the initial part of recovery. Therefore, riding a stationary bike without load along with isometric exercises for the lower extremities in the pain-free zone can promote recovery.