Pretty much every nursing school (assuming it’s reputable and not breaking the law) will require you to get a full physical, vaccines/boosters (if you need them), and titers drawn to prove you’ve either had a disease or have been vaccinated for it.
In Microbiology you should actually perform titer tests yourself (on bacteria, not your own blood!) but in case you’re not sure what they are: a titer test shows the quantity of antibodies present in an organism (in this case, you are the organism). Process as follows: doctor draws your blood, runs a titer test for Varicella (chickenpox) and you have antibodies present, which proves you either had the disease or had the vaccine. If for any reason your antibodies are too low or you have none at all, you will be required to have a vaccination, regardless if you’ve had one before or not.
SO. I went through this process a week ago and tried to find the cheapest way possible to do it (luckily, my insurance paid in full because it counted as part of my yearly physical). If for any reason your insurance does not cover these tests, there are websites such as these that are geared strictly toward nursing/medical students who need titers drawn. You can have all your major titers drawn for about $139, which is a great price. Basically you request the lab test from the company, they have a doctor write an order, you go into an in-person clinic and have your blood drawn, then they send you the results. Check it out!