Poor little mite!
My LO hasn't had a cold as such, but being a c-section baby was very snotty for quite some time. I used saline spray in her nose and it works wonders. It's a good idea to lay them on their side and spray it so that gravity helps

then keep them on their side for 30 secs or so to help them expulse it. You do need about 7 arms though lol
Hope she's better soon xxxx