My experience with respiratory infections being treated with antibiotics is that my insulin requirements doubled. As long as you’re willing to remain vigilant with frequent fingerstick testing, I would not be afraid to substantially increase your insulin doses. Infections can make a person with diabetes very insulin resistant. Keep your doctor advised.
Drinking lots of water and testing for ketones are also good ideas. I remember when this happened to me I would start to feel much better after taking the antibiotics for 24 hours. It was tempting to not finish the complete course of pills. Don’t do this! Always take the complete course of antibiotics unless your doctor tells you to stop.