Try the beta blocker for awhile as directed. Shift your training to endurance and strengthening rather than cardio. Give it a few months. Don't stress your heart further. Give it some time, then re-evaluate later.
I take a beta blocker occasionally for migraine and severe headache. For whatever reason these types of headaches don't respond to most pain relievers, but do respond to beta blockers, serotonin reuptake inhibitors, anti-seizure meds and other meds intended primarily for other purposes.
If I take a beta blocker I won't be able to reach my current max heart rate (173, at age 62), for a couple of days after taking a beta blocker. So I switch to mostly zone 2 and longer rides. And I have to go by "feels like," because my heart rate monitor might be telling me I'm in zone 3, but my feels like gauge is saying nah, bruh, this is zone 4.
Suits me for now since it's too hot and humid for hard training rides outdoors. If I feel like doing intervals I'll use the trainer indoors.
Similarly, my immunologist wants me to give up caffeine completely because I've developed an unusually fast resting HR (90s rather than the usual low 60s) and BP (150/90, rather than the usual 120/60) and way too many skipped beats, even at night, hours after my last cup of coffee. I checked the labels on all my foods, snacks and drinks and realized there was caffeine in most of my workout drinks and snacks. So while I was drinking "only one or two cups of coffee," in fact I was taking in the equivalent of more than a pot of coffee a day. So my presumed resting and max heart rates were skewed.
Also, FWIW, I find it easier to stick with my plan to emphasize zone 2 and endurance rides by switching to my hybrid. When I suit up for the road bike my mentality changes and I tend to push harder than I'd planned. But if I wear baggy shorts, a casual fit jersey and ride my hybrid with swept bars, I'll stick to my plan for an easier pace. I did 60 miles that way Wednesday and enjoyed it. Usually on the road bike in summer I'll keep ramping up effort and feel cooked after 20-30 miles.