Your fears are normal, but they're not warranted. This is something where a little bit of research can go along way in terms of recognizing real occupational hazards for healthcare workers. Here's the NIOSH site with what the CDC has to say regarding each state and needlestick injuries (there are also other links about bloodborne pathogens and their ease of transmission): CDC - Bloodborne Infectious Diseases - Overview of State Needle Safety Legislation - NIOSH Workplace Safety and Health Topic
It's worth looking into because protecting yourself and your patients from infectious disease transmission comes in various permutations. Hopefully learning about it now can save you future anxiety when dealing with blood and bodily fluids.
For now, let's consider the situation as you describe it. So, how does a glucometer strip work? It draws blood in by capillary action. Given the minute amount of blood the glucometer needs to do its business, it's unlikely that any is going to leave the tiny, tiny tube it made it's way into. The only risk would be if you were lucky enough to get a major blood drop that would run down the strip. This is not how you describe the situation so it's highly likely that the blood would remain contained in the strip.
Some nurses go faster and they do things without gloves that would make you think twice, especially handling blood, even if it's just a fingerstick. Especially if you're new, it's definitely likely to freak you out a little bit. But, try to always make sure that you're using your PPE and handling things in the safest manner possible. For now, that was more of a lesson that you're never too busy to put PPE on and you'll remember to keep your gloves on until you're absolutely sure you're done with everything.
Finally, even if there was some blood on the strip vial, the next person going to use it would definitely have stopped and wiped it off with an alcohol wipe before proceeding (hopefully -- and hopefully not without bringing attention to that situation). Also, if there was blood on that vial, your major bloodborne pathogens (HIV especially but HCV can hangout outside the body for some time and HBV a little longer than that) aren't usually thrilled to hang out on a surface exposed to air:
HIV In the Workplace | HIV/AIDS | CDC
HCV FAQs for Health Professionals | Division of Viral Hepatitis | CDC