Would a blood test show brain tumour?

Not likely : (unless it was doing something weird like pressing on your hypothalamus or secreting pituitary hormones). Brain tumors are suspected based on history and physical exam, confirmed with a head scan (MRI), and classified by a biopsy.

No: There's no indicators on routine labs, and there's no good tumor marker. Brain tumors announce themselves with new headaches, personality changes, seizures, and/or nausea / vomiting. They're quite uncommon at age 18. Don't discount either feelings / life situation or organic disease when you have a sense that you may be seriously sick. Stay proactive and discerning. Best wishes.