Suggest Treatment For Partial Tear Of Bicep Tendon At Elbow

Hello, I have a partial tear of my bicep tendon at the elbow. I have not had a MRI but have seen a sports medicine dr. I did this 3 weeks ago picking my 115 pound dog up off the ground to put him in my suburban and I heard a pop and have had a lot of pain since and sensation that my arm was on fire too. This dr I saw told me yes he thought it was torn but not completely severed off the arm. Told me to start arm curls with low weights for 4 weeks, gradually increasing the weight each week and to expect it to get worse before it gets better. My question I guess is should I just have surgery and have it repaired now without the risk of blowing it completely off out of the blue or is this arm curl type therapy really going to fix this w time? I use my arm everyday obviously but especially at work where I manage a liquor store and am moving boxes and bottles around constantly. Please, any insight is appreciated as I am confused w what I should proceed with. Thank you Mike