While there is no point in giving you medical advice online and no one can say whether it is normal for you, it is nevertheless possible (though not necessary) that the causes behind your elevated heart rate are natural.
Several studies, some of them referenced in Schuenke, Mikat & McBride (2002), have shown that human metabolism is much more active, even hours after the strength training. This results in a phenomenon called excess post-exercise oxygen consumption (EPOC). In a period for hours after the training the body will need to replenish body fuels (synthesize ATP), repair any damaged (muscular or other) cells, balance hormones and so on. All of these tasks require more oxygen intake than normally and this can lead to an elevated heart rate. (While the last inference seems logical to me, note, that I cannot provide scientific evidence that EPOC must lead to an elevated heart rate).
In short, one reason behind your pulse being higher than your pulse at rest could be that after a workout your body is not at rest. It is busy repairing and re-fueling your body!
Additional note: There is still a lot you can learn from your heart rate and monitoring it can be very informative. You just need to keep in mind that you have to compare your heart rate to other situations where you body was dealing with similar stress (and not to your heart rate at rest). If you do so, a high heart rate can be a sign that the training was more demanding than usual. It could also point at an approaching illness and be an indication of overtraining.
Nevertheless, you should always seek medical help off-line.