Can I still work out even with a slight sore throat and sore chest?

I have a slight sore throat and my chest feels alittle sore inside as well. I don't feel congested tho, nor am I coughing, but I constantly spit out alittle mucus that seems to build in my throat. The thing is, I'm on a diet and so far I lost 10 lbs in 3 weeks and I don't want to stop the diet until I've lost an additional 10 lbs. I've been on this diet shake that has helped me throughout this diet and I've been working out (jogging, stairclimbing, light weight lifting, etc.) as well. Can I still workout and continue this diet even with these symptoms? Thanks for you help.