Yup. Birds are reptiles! If you want to define a monophyletic clade that includes crocodiles and lizards, there is no way to do that without also including birds. To define a clade, you take the evolutionary tree and make a "cut" somewhere on it. Everything below that cut is part of the same clade, you can't selectively remove some branches but not others, unless it's by changing where you make your single cut.

So in this diagram:

The green circle notwithstanding, you would usually define reptile as a cut at the "C" on the diagram. You could put the cut at Lepidosauria, but that would mean crocodiles and turtles are no longer considered reptiles either.

A more zoomed-in look would show that after crocodiles and birds branched apart, you also get another branch where pterosaurs branch away from dinosaurs, and that birds are one of many branches and subbranches of dinosaur.