Baby has a cold

You just gotta keep him hydrated, keep clearing his air ways like you have been. Theres the phrase "sweat it out" but thats a myth that actually causes more damage than good due to it causing you to be dehydrated. Colds wont leave through your sweat but rather your sinuses, snot and phlegm. And only try to provide calpol if the baby has a fever, it wont help cure the cold only reduce fever and pain symptoms like a sore throat or headache. Try make sure all fluids are warm, provide warm baths.

You could also add a humidifier near where he sleeps or a steamy shower as well as an air purifier

I'm so sorry for you and your baby. It happened to me too. I used Oilogic Stuffy Nose & Cough, Vapor Bath & Essential Oil Roll-On. I feel it helped a lot

Please don’t do any bath if baby has temperature.
My eldest when she was 18 months old we decided to give her a warm bath when she had a viral infection, which raised her internal temp more and she then had s febrile convulsion at night due to her temp. Just focus on them hydrating often which helps

Cool mist humidifier is great, viks or snuffle baby, and hydrating

Plenty of walks, fresh air does wonders for baby. Also if you or your partner are having a hot shower, the person who isn’t showering can hold baby in the bathroom so the steam can help with any congestion x

I invested in a humidifier last winter because my girl had multiple colds and night time was the worst for her cough bothering her I also stock up on snufflebabe bath bubbles they’re like Vicks in a bubble bath. When she was smaller and still in her cot we propped one end up with books so it was on a slight tilt which stopped her getting all stuffy or having coughing fits when she was trying to sleep. Also second if you can get out for fresh air x