Hard mucus aka bogey and a cough in 6 month old

As the title reads, how do I resolve?!

I have that frida baby 4-in-1 tool for removing hard mucus in the nosey, but it’s a very hard device, and baby jerks a lot, so it has hurt her once when I used it, so have resolved to never use it. And now she remembers that, so she doesn’t let me come near her nose. Help

Secondly, she’s been having a weird cough. Took her to the docs 5 days ago, who said everything was fine, yet she still has the weird cough, where she sometimes coughs to the point of choking. What do I do.