When it comes to distance sports like cycling or running, there are a few ways to gauge progress. The first thing you need to do is establish a baseline. For example, cycling 5 miles at 15 miles per hour with an average heart rate of 160 bpm.

1. Traveling the same distance at a faster pace. Based off the example, you'd cycle 5 miles at 20 mph with an average HR of 160 bpm.
2. Traveling a longer distance at the same pace. Based off the example, you'd cycle 10 miles at 15 mph with an average HR of 160 bpm.
3. Traveling the same distance and same pace but with less exhaustion. Based off the example, you'd cycle 5 miles at 15 mph with an average HR of 150 bpm.
4. Any mix of the above. You're making progress as long as your distance and speed goes up while your heart rate goes down.

In your case, while you're maxing out your heart rate at extreme levels, you will need to know if your distance or power output in the cycling class is going up.

You don't have to do any kind of structured workout program, but it's really recommended. You do, however, have to record what your workouts consist of otherwise you'll never know if you're truly improving (it's really hard to be intuitive about it). As time goes on, you have to follow these basic rules:

1. If numbers go the way you want them to, keep doing what you're doing.
2. In numbers are flat or go down three workouts in a row, then assess:
3. If you're exhausted and feel beat, you're working out too hard. Pull back intensity and build back up.
4. If you feel fairly refreshed but just not meeting numbers, you've adapted too much. Increase your intensity.

For triathlon training, first you need to determine what kind of triathlon you're doing. You need to train to match the distance that the triathlon has. Sprint triathlons for example are only 12.5 miles on a bike where-as iron man triathlons are 112 miles on a bike. If you're already cycling the distance, then speed work is the focus (which looks like is what you're doing). Otherwise, you're going to have to slow down and start pacing yourself for longer distances.

When it comes to distance sports like cycling or running, there are a few ways to gauge progress. The first thing you need to do is establish a baseline. For example, cycling 5 miles at 15 miles per hour with an average heart rate of 160 bpm.

1. Traveling the same distance at a faster pace. Based off the example, you'd cycle 5 miles at 20 mph with an average HR of 160 bpm.
2. Traveling a longer distance at the same pace. Based off the example, you'd cycle 10 miles at 15 mph with an average HR of 160 bpm.
3. Traveling the same distance and same pace but with less exhaustion. Based off the example, you'd cycle 5 miles at 15 mph with an average HR of 150 bpm.
4. Any mix of the above. You're making progress as long as your distance and speed goes up while your heart rate goes down.

In your case, while you're maxing out your heart rate at extreme levels, you will need to know if your distance or power output in the cycling class is going up.

You don't have to do any kind of structured workout program, but it's really recommended. You do, however, have to record what your workouts consist of otherwise you'll never know if you're truly improving (it's really hard to be intuitive about it). As time goes on, you have to follow these basic rules:

1. If numbers go the way you want them to, keep doing what you're doing.
2. In numbers are flat or go down three workouts in a row, then assess:
3. If you're exhausted and feel beat, you're working out too hard. Pull back intensity and build back up.
4. If you feel fairly refreshed but just not meeting numbers, you've adapted too much. Increase your intensity.

For triathlon training, first you need to determine what kind of triathlon you're doing. You need to train to match the distance that the triathlon has. Sprint triathlons for example are only 12.5 miles on a bike where-as iron man triathlons are 112 miles on a bike. If you're already cycling the distance, then speed work is the focus (which looks like is what you're doing). Otherwise, you're going to have to slow down and start pacing yourself for longer distances.

EDIT:

Regarding whether or not you're going to hard, the general rule-of-thumb while training is to train at 70% of your effort. The idea is that you progress more steadily at 70% without destroying your body and over-exerting. This allows you to train for longer periods of time without forcing a deload or risking injury. Typically a training block lasts 4-8 weeks. You're training too hard if you burn out in 2 or 3 weeks.

But those are just guidelines. There's no reason to change if you're making progress.