I would first check if you have selected radiological or neurological view. Radiologists imagine they are viewing a patient who is on a bed from the position of the feet (so patient left is on the right). The neurologist imagines they are viewing axial slices from above the head (so patient left is on the left).
Here is advice for MRIcron. First, use View>FlipLR menu item to toggle between radiological or neurological orientation. Second, Help>Preferences provides checkboxes:
a.) If "Reorient images when loading" is checked, the images will be resliced, similar to SPM. This is nice for viewing, but is often not good for drawing regions of interest (as screen pixels do not have a one-to-one correspondence with voxels).
b.) If "Rotate to Nearest Orthogonal" is checked the image is losslessly reoriented to approximately standard space. This is my preferred way to view data, but things can look a little odd if your images are very anisotropic or acquired at an oblique angle.
c.) If neither of the above options are checked, the image is not loaded at all - this simply shows how the data is stored to disk, without any spatial transform. I would only use this is you are trying to work out EPI slice order or something like that.
As long as you have selected option a or b, an easy way to determine left and right side is to look at the XxYxZ coordinates shown in the title bar when you click on an image. The first (X) value should increase as you move left to right.
While MRIcron is a mature and robust tool, be aware that beyond maintenance it has not been updated since 2010. You may want to try out my more recent software
With MRIcroGL you can use the Help>Preferences (or MRIcroGL>Preferences if you use MacOS) window to choose between radiological and neurological orientation. As long as you have the View>TextAndOrientationCube menu item checked you should see a "L" or "R" shown on your images to remind you of the display. If you do not see this, it suggests that your image does not accurately describe space (you can use the Import/ConvertDicomToNifti menu item to convert your data with accurate spatial transforms).