Sounds like you need a new fan to me.
Or a new ceiling fixture if you don't use the fan (though I think everyone should have fans EVERYWHERE! They are so useful.)
An electrician would probably just tell you the fixture is bad and needs replacing. Do you have friends or family that could help you replace a fan? The fan itself should be ~$100ish from any big box store. Assuming the old fan was installed correctly with a fan brace it's about an hour job to swap in a new one.
My in-laws had a ceiling fixture where half of the bulbs never worked. I replaced it for them last year and it was all burned up inside, but they'd been using it for years. Half of the lights had shorted out, the other half were fine. So if you are okay with only half your bulbs working you could just continue your life as is.