A Bun with unusually noisey breathing needs to be examined by a Vet. Respiratory Tract Infections do not always present with a nasal discharge, especially if a the infection is in the lungs. RTIs can become very serious so I certainly would consult a Vet ASAP. It may just be that he was hot and hence his respiratory rate increased but its better to err on the side of caution and get him examined.
Its generally not advisable to bring outdoor Buns into a warm house and then put them out again. They dont cope well with extreme changes in environmental temperature and that alone can bring on a RTI.
Lots of things can cause runny eyes. Infection, an injury/foreign body in the eye, dental problems where the tooth roots have elongated and block the nasolacrimal duct. Again this is a problem that you need get checked out by your Vet