This might sound harsh, but if you don't know how to manage your time, you won't survive a career in medicine (or anything that requires juggling multiple responsibilities at once). Medical schools may question your passion for medicine if they see you starting extracurricular engagements such as volunteering/research/etc during your senior year. Although I don't think this is your intention, you may come across as someone who wants to go into the field of medicine without understanding what it is, and threw in some extracurricular activities halfheartedly at the end of your college career just to get into medical school. A 4.0/35+ on the MCAT isn't enough to get you in anymore.
Start off volunteering somewhere in a free clinic, hospital, or other health area where the time commitment is fairly low (3-4 hours/week). You should definitely be able to manage that commitment on top of your schoolwork (many students do more than that on a regular basis). Other options include volunteering with a crisis helpline, where you may be able to take calls on your phone and "work from home" while studying. And don't be afraid to utilize your weekends for volunteering, if that is a possibility. Also, use any upcoming breaks (especially winter break) to shadow. While shadowing isn't always a hard and fast requirement, you need to know what you're getting yourself into. Start off by asking your PCP if you can shadow him/her, or if they can connect you with a colleague. If you go to a school with an affiliated university hospital, you can start there too.
If there are other volunteering opportunities in your area that are of interest to you and aren't a huge timesuck, you can try those too (your volunteering experiences need not all be clinically related...you just have to show that you like helping people). Free food banks, soup kitchens, Habitat for Humanity, tutoring and the like come to mind.
Since you haven't had any experiences until college, I would recommend taking a year off to pursue certain clinical activities (mentioned above) to really demonstrate that you are committed to going into a career in medicine and that you know what the field is like. Many hospitals do hire students/recent grads in unlicensed positions (PCAs, patient transporter, etc), which may help fund your year off if that comes across as something you want to do. PM me if you'd like help in identifying other resources in your area.