He certainly can sleep with you. What he has is in all lieklihood not contagious to you.
As for your other dog, if he is not showing any symptoms of illness, then he does not need to see the vet. Most of the time, these illnesses are caused by viruses, which antibiotics can do nothing to fend off. The antibiotic is usually given only to dogs that are already showing symptoms to help clear up and/or prevent any secondary bacterial pneumonia from occurring. If your second dog is not showing symptoms, the vet won't really prescribe anything for him.
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