Hi there. Wow, impressed you are running! And happy you are staying fit. Congrats on being a cancer survivor! Awesome. I do think that your heart rate is a bit too high. Please see your doctor about this to further discuss if it is safe for you. I'd not run until you see them. good luck and please come back and tell us the outcome of your doctors visit.
Hi, no offense meant but are you sure that your rate is being measured correctly? There is a physiological general rule of thumb that the max heart rate a person can achieve while really really trying to get it as high as possible is 220 minus your age. So an out of shape 20 year old can get to 190 just from climbing steps, but a 68 year old in great condition can expect to get up to approximately 152.
Kudos to you on what you'e doing. Assuming you've been cleared by a doc, a thing to watch for is irregular beating during exercise. Also make sure your heart rate declines normally after you stop. Hopefully you're also acquainted, just in case, with the signs for female heart attack which can be different from male.
Btw I'd also want to be having an anti-inflammatory lifestyle, especially in eating, to lessen any chance of artery plaque rupture or erosion. Having asthma probably means you tend toward over inflammation.
What is your resting heart rate?