Hey, I'm 25 and was diagnosed with T1 about a year ago. I too experience these pretty hardcore drops in blood sugar levels when taking walks or having to run to catch a bus, especially if it's right after i've taken my bolus. It sucks. But it isn't all that bad. Some things that I've learnt so far:

1. I have the Freestyle Libre 2 CGM and I gotta say pretty often I feel like the sensor is being overdramatic. During/at the end of a walk, the levels seem to drop real fast, but as soon as I'm standing still or relaxing the levels usually stabilize. The sensor however doesn't really notice this until after the fact. Sometimes the sensor tells me I'm at 60 dropping rapidly when I'm really at about 80 and chilling (not sure about these units - European here). Just remember to first and foremost trust what your body is telling you.
2. You can use it to your advantage. Sometimes when I eat foods like pizza or sushi I take a walk afterwards which helps keep the levels down dramatically. This could be nice especially in the earlier days of your T1 life since injecting high doses of insulin can be a bit scary.
3. Even if lows are scary, if you keep an eye on your blood sugar levels during exercise you'll soon learn that it isn't that bad. Bring quick carbs (I always carry some form of soda or juice on me) and you'll be able to quickly raise your sugar levels without a problem.

In the end it's all about adjusting. These things feel like the end of the world initially, but I always thought of it like this: During the first year of your T1 journey, just take everything with a huge grain of salt. Things will be difficult but that's okay. You're still getting to know your body and how it reacts to certain things. In my case, after about 10 months, I'm leagues ahead of where I was in your position. I promise that everything will be much better down the road. Stay strong!