POTSies can have their hr go up without feeling dizzy or faint. Indeed, some POTSies never faint! Also, your bp does not have to go low to be diagnosed with POTS. Yes, your hr is going up to maintain bloodpressure when one has POTS, but the heart can maintain the bp or the bp could even go up due to the heart working to keep the bp from dropping---I hope that makes sense.
Worrying about if you are going to be ok when your heart is doing erratic things is certainly a good reason to feel anxious or stressed---after all, it is your heart. But since the autonomic nervous system is involved, physiological symptoms that LOOK like anxiety can also present themselves without being the actual psychological anxiety that many people think of. It is beneficial for POTS patients (and probably everyone in general) to read about and understand the vagus nerve and its many roles in the body system.
There is an excellent POTS group on facebook with thousands of members and tons of support and answers to questions you may not even realize you had. It is the group with POTS spelled out in the main image with black, white and turquoise colors.
I encourage you to get a notebook or something to track when your heart rate is going up. Maybe even get one of those finger monitors that does hr and oxygen (like they have in most doctor's offices and fit in the pocket), or a Fitbit that actually works, so you can track the date time and activity you did when the hr went up. This info is helpful for your doctor and for you understanding how your body reacts to things. Like, if you have POTS you might discover your hr goes up when you step out into hot weather, during a hot shower (that is stimulating the nervous system in a ton of ways), or after you eat and your body sources blood to your stomach for digestion. Each case can be different!
Good luck and know there are a ton of people out there with POTS who are happy to answer questions if you join their groups. They will say if they do not think its POTS too! But not every doctor is knowledgeable on the subject unfortunately.