What has she been eating in the last month? Some chicks are born with something wrong and do not thrive, and fade out in a week or so, but for her to come to you at 6 weeks- and not get bigger over the next 4 weeks is odd. Do you have other chickens, or just her? If you have others, are they all ok?
If she is not eating a *fresh new bag* commercial chick starter (not scratch), get her on that asap.
Where did she come from? A commercial hatchery, feed store, or neighbor/friend?
If this is a weak bird from from a dietary problem, the respiratory problem may clear up on it's own as the bird gains strength. If she does not have oral, nasal or eye discharge, this probably is not an infection. It may be mucus in a weak bird. If she does not have a *bacterial* infection, antibiotics will not help her, and giving her tylan injections is just going to add pain and stress to her already tenuous existence.
From the photos- she really looks like some of the chicks I have seen that have been fed only or too much scratch or old/stale vitamin depleted starter.
Is her beak flexible, ie can you bend the end?
jess