How do I get rid of really bad cramps without medicine?

Well, without medicine they won't go away completely, but a warm bath or a moist heating pad will certainly help quite a bit.

I do not like to take meds either. I using breathing and calming myself down. I sit or lie in a quiet room and concentrate. I like to be alone when I am in pain. I close my eyes and breath in deeply through my nose as much air as my lungs will hold and slowly expel it from my lungs through my mouth. It usually takes me around 5 minutes to start feeling relief. But I have been doing this for about 15 years.

I find exercise (even though it is the last thing you want to do) really helps as it increases your circulation. Or here's a odd one - a cat. They are nicely warm and if you can get them to sit still long enough it's brilliant, especially when they purr. Weirdly enough best water bottle I've ever had. A bit silly I know but my first suggestion is a proper one.

Sometimes it helps to pull your knees up to your chest, sort of like the fetal position. A heating pad can also quickly become your best friend. I've got one with a timer and about a million different settings - it's great.