Being a small female I have always had a higher than average heart rate with issues of feeling as though I will black out upon standing. The fast rate and near syncope generally happen when my bp is on the lower side. The best advise is to try and rise more slowing and add some salt to your diet if your doctor deems it OK. That said, if you are experiencing more troubling symptoms like shortness of breath and the tired feelings I think it prudent to at least consult the doctor. They may tell you everything is fine but I think it better to have a doctor check you out and tell you all is fine then to not go and let things possibly get worse if there is an issue. So don't fret about going if your symptoms are new and not normal for you. Better safe than sorry I say. Take care.
I read you to say your resting HR is near 100. And a BP "lower than normal" isn't very descriptive. That said, given those numbers all I'd have is a wild guess anyway.
If you have problems with blacking out, not just a little dizzy, when rising you should discuss with your doctor. I'd start with my primary care unless my BP was real low and that is a relative subject, personal subject, not a "normal" one. Some people get by with a BP in the 90/60 range. When I was taking heavy doses of beta blocker to lower my HR and got that low I would be dizzy easily and if I got up and started walking immediately I could feel a blackout coming. I'd stop and lean into a wall and it would pass. I was later changed to a lower dose of BB (now 50 mg, down from 200 mg) and a calcium channel blocker was added. Now my HR is around 80 when at rest and my BP is always a little below the 120/80 "Normal". I often take a BP reading when at Walmart. I assume their machine is reasonably accurate.
Well, those are my thoughts, hope they help you decide to discuss with your doctor if the symptoms don't disappear on their own.