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Nose bleeds aren't a symptom of an aneurysm. Some tiny minority of people with aneurysms will experience a sentinel headache as a sign that the aneurysm is leaking prior to its bursting, but most people have no symptoms until it ruptures. Here is some more information about brain aneurysms:
You should definitely have your headaches and nosebleeds evaluated by a clinician to make sure they are not the result of some serious pathology.
There is no time limit for a sentinel headache. They can occur off and on for months before the aneurysm bursts. What you are experiencing is most likely a sinus headache. A sentinel headache is "the worst headache you've ever had" not one that is mildly annoying.
To help with the nosebleeds until you see your doctor later this week, you can use saline nasal sprays. You can buy these at the pharmacy or make your own at home with 1/2 teaspoon salt dissolved in 8 ounces warm water. Put it in any old spray bottle that you've cleaned thoroughy and spray several times a day. A humidifier, especially in your bedroom, can also help prevent irritated nasal passages.