You do not need a prescription, but the pharmacist needs to to "approve" as it is an over-counter-drug. So basically you need to tell them you have Type 1 and that you are not using insurance. (My pharmacist bugs me to get a prescription every few years in case he is audited by my insurance company.)
Also, because Fiasp is new, not all pharmacies have it in stock. You may want to call around or visit one of the big-box pharmacies.