I also have had a fever for past few weeks, tiredness, the painful neck and generally feeling unwell. I had a full blood count done a couple of weeks ago and a test for glandular fever and apparently everything came back fine. they also did a swab in my throat and that is fine.
Federal laws do not address how many hours an employee must work to be a full-time employee. It leaves that decision to the employer. Some state laws, such as California, recognize employees who typically work at least 40 hours a week as full-time employees. You must pay all employees covered by the Fair Labor Standards Act overtime pay for any hours worked over 40 in one week.
Part time is a label. I worked a job where they said I was part time, to keep me from getting benefits, even though I was working 40 hours. Since benefits are a company choice and not required by law, they can set the rules of how many hours you have to work to qualify for benefits. Most companies set it at 32, but I've seen better places say anything over 20 qualifies for benefits. The employer decides what is part time.