A bleeding nose during an upper respiratory infection is common. I would only see a doctor if the bleeding nose continuues for more that 15 minutes. If it is occurring only when forcefully blowing your nose, it is not of concern unless it continues well past the resolution of your cold.
As you recover, the use of a saline myst or nasal spray may help with your symptoms. The head pressure you describe is common in sinus infections and a nasal spray would be beneficial for that as well.
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