charger won't stay connected and charging

I just replaced a worn charger thinking it would solve my issue, but it hasn't. When I plug the charger into the side of the MacAir I have to fiddle with it up and down to get it to connect and properly charge, and then it will sometimes lose that connection so I will get a prompt that my battery is low again.

I have tried using a dry, clean toothbrush and scrubbed the new charger and charging part on the side of the Mac, but it did not improve the problem at all.

I've looked in the guide to see if I could replace that part, and I do not see it as an option.

Please help