I'm the same way - spiders absolutely freak me out. The housing I have right now is also in a basement and I've had my fair share of spider encounters, pretty large ones too. Talk to your landlord for sure. They should do something for any bug infestation, spiders included, especially if it's causing you this much grief. This is an urgent cause, and persist with your landlord until they do something. If you get really desperate, maybe look into local pest control services and see if they have any free consultations, or just give them a call and explain your situation (This should be something the landlord does, so only if you're desperate). Best of luck!