Yes, they generally say to sleep on your left side, when pregnant.
If not, try sleeping sitting up in a comfy chair. When I was farther along in my pregnancies, sometimes this is the only way I would be comfortable, to then sleep. Because my gigantic tummy, was so uncomfortable.
Or, if you have or can get a "wool/lambswool" type of rug... sometimes they sell them at Costco, but its expensive... this can alleviate some body soreness/pains/bedsores in people who are bedridden, for instance. Because "wool" breathes and is either cool or warm, and adjusts to the body. It is recommended in some hospitals for this reason, as it prevents bedsores for example, in people who are confined to bed.
Or, try asking your OB/GYN....
Or, use a "body pillow" to put between your legs, when you are on your side, to help support your body/tummy. This is also what I utilized, and helped.
Oh, sorry, I just saw that the body pillow is not helpful for you.
I know, its not comfortable, just some things that I tried, or have heard of.
As a side note, per your saying you feel like you are being "squeezed hard": sometimes "Braxton Hicks" contractions... will feel like your tummy is rock hard... and it gets uncomfortable/tight feeling. But this is a normal part of pregnancy, I forget from what month it starts. Perhaps ask your Doctor.
ALSO, with my first pregnancy, my daughter was more active at night... and in conjunction with Braxton Hicks contractions, it was so uncomfortable to sleep.
All the best,
Susan