Trouble producing milk

Hello everyone! My baby was born 2 months premature and is 4 weeks old today. I am trying to pump to give him as much breastmilk as possible, but he is eating 2.5 ounces every 3 hours. I am supplementing with formula but I am lucky to get 1 ounce with each pumping. I do try to do every 2 hours and have even started handpumping between sessions. I have also been eating lactation cookies. It seems like my supply has actually gotten smaller, as I was getting about 2 ounces. I don't know what to do. Wood it help to try actually putting him to the breast? I am a bit nervous about trying that as he eats fine with a bottle. Any suggestions would be appreciated!