Am I working too hard?

Its obviously not 166 if you hit 168.  You won't cause any damage to yourself hitting your max HR.  If you do some searching, you can find some methods for testing to find your approximate max HR.

First, a "max heart rate" or "zones" constructed by any formula is not going to be specific to you, but only "kinda close" to you.  The "mhr=220-age" formula takes only one vague datapoint (your age) so is by definition a very broad rule of thumb.  There's an updated version - 206.9 - (0.67 x age) that has been shown to be closer, but still takes only one datapoint.

The Karvonen fomula takes two datapoints (your age, your resting heart rate) and will be a bit closer.  There are a few other adjustments that can be added to this ("-5 if you are sedentary, +5 if you work out twice per week") and all that, but again it's just a formula.

If you really want to determine your ranges, then you need either a field test protocol or a medical test protocol.  Either go run on a track with an HRM, follow the protocol, and calculate your ranges, or visit a sports medicine clinic, get hooked up with a mask, run on a treadmill, have them measure your oxygen intake, take blood samples once per minute, and so on, and voila - you get accurate numbers specific to you. I recommend the field test protocol and there are several articles on BT on how to do this.  Until then, go with the Karvonen formula for your MHR and zones.

A a high heart rate at a relatively low level of exertion is to be expected for someone with poor overall conditioning and not much experience.  A beginner triathlete, in other words.  To explain:

HR is a lagging indicator of the workload put on your body:

• Your brain says "muscles, do X (climb this hill, swing this hammer, run 10 minutes per mile),
• your muscles say "heart, I need Y amount of oxygen to perform workload X", and
• your heart responds by "I'm going to beat at Z beats per minute to send Y oxygen to you, muscles".

And thus you're climbing that hill, swinging that hammer, or running those 10 minutes per mile.

If you are well trained, have a metabolic system that produces energy efficiently, and have good running or cycling form, then to perform workload X you will need less oxygen Y and thus a lower bpm Z.  If you are out of shape, have an inefficient metabolic system, poor form, etc, then your heart rate will be significantly higher in comparison.

You're saying you feel fine but your HR is really high.  How you feel is often called RPE - rating of perceived exertion.  Here's a good chart that explains (I like the 10 point scale, there's another with 20 points I don't like): http://sbrworkouts.com/rpe-scale-description

Based on your description above, I'd say you were climbing the hill at RPE 8, maybe flirting with 9, and thus it's to be expected your HR was nearing your max HR because you were in zone 5 which tops out at your max HR. 

And that all makes sense: your HR is matching your level of exertion fairly closely.  If you really want to climb hills at zone 5, go for it but it's a pretty tough workout, you might want to consider climbing at zone 4 or a little lower end of zone 5.  You said you're the 100% type and it sounds like it.

Don't sweat the HR values. If you're about to keel over, your body will let you know. As others have said, experience will gradually teach you what your real MHR is. You'll also find that on hot summer days, especially if you get a bit dehydrated, then your HR can get surprisingly high.

Having said this: you mention that you "truly believe you have to give 100% every time to achieve results". Now that sounds like a nice slogan, it exudes toughness, but it's not really the way to get results in S/B/R. Training smart, and training consistently, is more important than training hard. It's important to mix up the distances and intensities in your training, and recovery is a key element of the training -- that's when your body adapts. If you want to burst a vein or two, focus on the bike for that for now. For the run, not so much. 

Good luck.

My resting heart rate is 53, my age is 47.  The highest HR I've seen is 203, so the max formulas don't work well for me.

And yes, if every single training session is 100% effort then you are training too hard.

I lack the expertise to speak to the heart rate issue, but as an aside, I'd strongly recommend you carry a flat repair kit/extra tube and practice fixing flats.  It's just a part of cycling.  IMHO.  LOL.

According to charts, my max HR is 165, but I frequently peak in the high 170's during workouts.

First, congratulations on your commitment to take control of your health and fitness.

The answers to your HR questions are here (this thread should be manditory reading for all newbies):

http://www.beginnertriathlete.com/discussion/forums/thread-view.asp?tid=25733&start=1

As far as your flatting problems, the first thing that comes to mind is that you're having pinch flats.  What air pressure are you running in your tires?  Need to make sure you're keeping them pumped up.  I also second the suggestion to learn how to fix a flat tire.

It sounds like you were in great shape when you were on active duty.  You didn't get out of shape overnight, so you need to stay patient as you work to regain your fitness.  If you are consistent with your training and stick with it, results will come over time.   Consistency is the key.

You didn't mention anything about your diet in your post, but I assume you are giving that as much attention as your exercise program. 

Good luck to you.

Mark