My baby girl is having a cold too :(. I heard baby colds can last many weeks so nothing much we can do but hang in there. I agree 3 months is a bit young to take medicine. I use a baby nasal spray Sterima, both Watson and guardian have it. Spray both nostrils then use a nose sucker to suck out the mucus. I have to do it 3-4 times a day but the mucus keeps coming back. So sad to hear her strained breathing but not much else we can do :( hope they will get better soon!
At 3 months old, pls consult your pd for better advice. Here's a link that could help you : https://www.healthhub.sg/a-z/diseases-and-conditions/691/common-childhood-conditions-coughs-and-colds. Hope she recovers soon:)