I had my left common carotid artery, including internal and external sections, completely removed, and remaining sutured and clamped in 2013, meaning I only have blood flow from my right side to the rest of the head and neck, and was never told of any exercise restrictions, other than starting out slow and going to rehab first before starting out a very basic indoor exercise routine, I'm not running though, when I asked, which is a joke compared to what I did before cancer, but that's mainly due to the chemo in 2009, and is what it is now. Due to some other surgeries, and side effects, I see a cardiologist who has performed a series of tests including 3D carotid ultrasound, EKG, ECG, stress test, which came back clear except for the left carotid defect, orthrostatic hypotension. I'm also closely monitored and tested by my other doctors, maybe 7 lol, so I feel confident there, but you may want start with your doctors for further insight that may pertain to you. One thing I have noticed, which may also be due to other structures removed like the sympathetic, spinal accessory, vagus nerves, and veins, I no longer sweat on my head, neck, face, very slightly on the arms, if any, even in this hot weather, so I'm always carrying water, try stay aware of the fact. I should carry some type of alert bracelet or something as I have no left neck pulse if it's taken there, but such was never suggested, and it's not like I need approval either.
Good luck, but it sounds like you're doing well.