New job, but way too sick to go into work?

My advice is to call in sick. If you are as sick as you say, you should not be working with food and customers. Don't leave it until too late, give them time to get someone else in for your shift if they need to. Explain to your manager how sick you are and that you are going to the clinic/doctors tommorow . Ask them if they would like you to get a note excusing you from work (so they know you aren't faking it). You might want to get one anyway, just incase.