I'm a nursing student also, and have been a Type 1 for 8 years now. I was also on MDI for 5 of those years, but have now switched to an insulin pump. I thought it would be really hard, but it has been a God-send. I don't have to eat - that is the best thing, because you know how erratic the times are that you can eat. When my basal rate is set correctly (and that takes several months of playing with), my blood sugar doesn't fluctuate more than 30 pts up or down. Then when I do get the chance to eat on my clinical days, I bolus for whatever I'm going to eat in terms of carbs.
The pumps are expensive, along with the supplies, but I'm lucky in that my endo got me approved quickly. I don't know how I would manage doing what I'm doing - even just doing clinicals a couple days a week - on MDI. Is it possible to set up a schedule of some sort with your employer, where you are given time and space to test/eat on a set basis? I know easier said than done, but it might give you a starting point.
In terms of testing, that has been a LOT harder to deal with on clinical days (same hours as a nurse though, so I do know how hectic that can be). I have a very small meter which fits in my pocket, and got one that tests in 5 seconds, but I don't bring my logbook. I just record from the meter later. It's a PITA to carry though, and sometimes with the extra weight of the meter and glucose tabs I feel sort of lopsided with my scrub top. I may get a simple belly pack for around my waist. I can't see why they wouldn't let me.
As for getting down that low, I've used the glucose gel (looks like the Cakemate gel frosting tubes) several times, and that seems to work a lot faster on a low than glucose tabs or regular juice/soda. I also find that non-diabetics have a very hard time understanding the feeling when you get that low. When I get into the 30's, I actually fall out of the "low" feeling of jitteriness and muddled thinking, and into a serene calm KNOWING I'm low and have to eat, but can't, because nothing looks good and I'm going to get fat and the bread is white and I only eat wheat....etc. It's downright SCARY after I come out of it, that all symptoms of the low had passed and people would think everything was alright, but I'm definitely not alright.
Please know you're not alone. A lot of what you go through will be trial and error - for quite a while, unfortunately. It may mean switching to a basular insulin like Lantus, then taking a short-acting like Novolog when you do get a chance to eat. I did that for a while before I went on the pump.
Feel free to PM me if you'd like.