Hospitals are migrating to EMRs now, written notes will hopefully be obsolete in the next few years. VAMC hospitals' charting has been electronic for decades.
As noted above, pretty much all notes will be typed in the next 1-5 years. In the interim, you can do what I did...make a Word template that approximates your hospital's Progress Note paper, type your notes then print on chart paper.
Not only will handwritten notes become obsolete, but potentially illegal...e.g. in Rhode Island there's a bill under current consideration which proposes to prohibit all handwritten medical records and notes.
OP: if your hospital doesn't use an EMR, there probably is already a template for people who prefer to type their notes...ask what you're allowed to use. (E.g. when I was a third year, we were banned from using the templates because they wanted us to demonstrate we could write notes on our own and to make sure we went through the process of thinking about vitals/labs/meds rather than just importing values. It's unclear to me what level of training you're at, but just ask the others in your program.)