Rather than a cough syrup you could use a sore throat gargle so you don’t digest it. I find the Betadine sore throut gargle quite good.

Read the label, it should advise you there. Cough syrup is pretty useless so I dont know why you would think you need it

Also check with a pharmacist, is a good idea when it comes to any medication.

Best to check any medication with GP.

Personally I think it’s questionable if cough syrups really help. Certainly during pregnancy you could look into natural remedies. https://www.healthline.com/health/allergies/best-natural-cough-remedies#marshmallow

Check with gp or ask at chemist. I think you should avoid any medication while pregnant or breatsfeeding.