I do some mindfulness. Paced or square breathing, progressive muscle relaxation. The great thing about these is that the more you practice them, you'll find you can do them anywhere.
You may want to do some research on the subject. Most people are aware of MBSR (Mindfulness Based Stress Reduction) as it's benefits are highly publicized. Less well known are the negative aspects of meditation especially in practitioners with trauma, anxiety and depression.
Sleepiness isn't a negative side-effect unless you're meditating while driving.
It's actually not crazy: it's quite understandable.
In meditation we're asking our mind to do something it doesn't regularly do: concentrate on one subject. This can lead to unexpected results. Especially if your good at it.
In the East, meditation isn't used the quell anxiety. Only, recently, in the West has this been the case. And we don't have the experience of the East. We don't have the history. We don't have the support systems in place when meditators reach difficult territory. When we see things we're not ready to see because our concentration is strong. When we develop insights we're not equipped to handle. When we don't have a teacher to guide us. When we're not even considering enlightenment.
The sleepiness you're experiencing may be called 'dullness' (sloth, torpor) in the Theravada Buddhist tradition. It's one of the five hindrances to be overcome in meditation. I can't say that's where you are from your post, but if you're experiencing increased anxiety from your practice then I would put the meditation aside.
Yoga can be one form of moving meditation. In a class? Maybe not do much. Meditation is all about paying attention. If you make coffee or breakfast in the morning try doing it with purpose. Slow down and appreciate each step as you do it. Notice. That is meditation. Jon kabat zin is a good person to read.
For me reading the books of Ekhart Tolle A New Earth and Power of Now helped me understand the mechanics of the mind. He has lot of pointers on how to be present. Probably you could relate, most do things mechanically. Like taking a shower. But the mind is already in the office. We could be in the shower mentally and physically, listening to the water flowing into the drain, smelling the deodorant.... .Or while at the breakfast table be aware of what we eat instead of watching TV not focusing on what we eat.
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