Over worried mum?

My 13 month old had a cold the last week and a half. Wet cough snotty nose etc, for about three days max the cough wasn’t as bad and the snotty nose went.

Now he a really snotty nose and a horrible dry cough and hoarse voice.

I didn’t go to the doctor before because I though it’s just your standard cold. But now I’m spiralling is it normal for them to get sick straight after being sick? I hate seeing him so unwell. It’s making me paranoid why js his immune system soo bad