Coughing in Pregnancy

Hi everyone, I am 16 weeks pregnant. This is the 3rd time in about 5 weeks that I’ve had a chesty cough. I seem to get a week of no coughing then it comes back. The first time I had it I felt quite unwell and my chest was sore. I went to doctors who said just viral. The second time and this time, I don’t feel at all unwell. It is just annoying more than anything. I have asthma and the doctor did say asthma can get worse during pregnancy but I am not wheezing or anything. It has got to the stage where the cough is waking me up at night and I’m worried that I am hurting the baby from coughing so much. Is this the case? And has anyone ever been in a similar situation where a pregnancy symptom is actually a reoccurring cough??