Cough syrups not recommended at this age..only nasoclear saline drop 2 drops in both the nostrils every 4 hourly for 3-4 days is sufficient. If cough is worsening then nebulizations will be required.
Any temperature more than 99.5 degrees is considered fever and any fever spike below 3 months requires blood and urine workup and plan antibiotic accordingly.
Next Steps
Watch for danger signs like breathing problem, dull activity, poor feeding, decreased urination; if present then please visit nearby hospital for further management.