Saline drops; 3mo old mucus throat

Hi so my baby had some real big boogers in both his nostrils. I used a couple of drops of little remedies saline drops in each nostril. One booger came out but the one from other side didn’t. But now it sounds like he has phlegm in his throat!!! Kinda like when you’re sick and your voice changes.. in spanish I’d say he sound rronco.

What can I do to clear the phlegm in his throat?!?!

Also any other ways to get boogers out of his nose that won’t make him scream bloody murder?