Even if recommended by your doctor, it is always your choice to have or not have surgery. But, it is important to understand the possible consequences of delaying or declining surgery.
Because ACL reconstruction is an elective surgery, there are no serious or life-threatening consequences associated with not having it.
However, if other treatment methods have failed to improve your symptoms, the likelihood of them getting significantly better without surgery is slim. In fact, your current symptoms will probably remain the same or even become worse.
Furthermore, since your ACL is torn, the normal anatomy of your knee is altered and this can lead to other problems such as meniscal tears and early arthritis simply because the knee cannot function correctly without an ACL.
The final decision to have or not to have surgery rests with you, but all concerns related to this decision should be discussed with your doctor at length. Then you and your doctor can come up with a treatment method that is comfortable for you.