It has been stuck for a few weeks, and I'm scared to put too much pressure on it because I don't want to break either lens or camera body. Should I go to a camera shop to see if they can do anything, or should I buy a new body for all my other lenses?
A lot depends on the camera type and lens type. The short answer is you probably need to take it to the shop. As a longer answer my story of the last time it happened to me:
I have a Nikon and had a teleconverter get stuck on a D800 body. Think of the camera lying on its back with the lens pointed at the ceiling. On Nikons, there is a small pin that extends upward from the body into a slot on the lens that keeps the lens from rotating. The release button retracts the pin. If the pin breaks off of the retraction mechanism, it can be stuck up in the lens, the lens cannot rotate out of its bayonet connection so is stuck. But the lens itself is not stuck -- heating or turning harder will do no good, the PIN is stuck.
With that specific setup, there are a few possible DIY repairs. One is to literally sit the body and lens as described, rotate gently back and forth, and the pin may fall back into the body by gravity. In my case it would not, but there was a small rubber gasket around the lens-to-body attachment, and if lifted up (e.g. a small screw driver) you could see the pin physically going up into the lens. In my case I took a needle (literally a sewing needle) and poked the pin near the lens, pushed down, and repeated over and over. It moved just hundredths of an inch each time, but after a few movements, it came loose, fell into the camera - lens came off. THe camera had to go back for repair anyway as the pin was broken, but I could keep using the lens (well, teleconverter in this case). However, I looked at some other lenses and the pin was not visible, so even in my Nikon case this varies by lens.
You need to know for your particular camera how the lock mechanism works, to know if a similar solution is possible. However, regardless, it is quite likely that even if you get the lens off, either the mount or the lens will need repair. While remotely possible it is a case with simply too tight of a connection, it is more likely that the locking mechanism has broken in some way, and so even if you separate them, you will need a repair. Either the next lens will get stuck (or not lock) on your body or the same lens will get stuck (or not lock) on a different body.
Almost never is the solution more pressure. I have yet to see a DSLR that had very tight connections - all I have seen have some locking mechanism, and usually that breaks to cause this. You may have an exception, but I would bet against it. In other words, the simplest may be to send/take it in for repair with the lens attached, as you are likely to end up there anyway.
I had a similar problem: I basically had to force my camera lens off the body. It was a bit of a risk because I could have broken my camera and my lens. Fortunately it worked. After looking at my camera lens mount, I noticed one of the screws was loose. I tightened that bad boy up, and the problem was solved. I do however agree with @Linwood's answer. It is probably a better idea to take it to the shop.