Don't bother with paying for Tylenol PM. The "PM" in Tylenol PM is just an antihistamine -- it's diphenhydramine HCl,
exact same drug as Benadryl, so each capsule is the same as taking 1 (25mg) Benadryl + 1 (500mg) Tylenol...and unless you're in pain, you don't need the Tylenol part. (Nyquil, for all y'all green liquid junkies out there, also contains an antihistamine for the nighttime sedative part -- doxylamine succinate.)
Best option in lieu of Tylenol PM? Whatever store-brand generic "sleep aid" or "antihistamine" formulation contains doxylamine or diphenhydramine. Cheaper, and just as effective.
Though, I like melatonin best to get to sleep. No hangover feeling like you can get with antihistamines or other over-the-counter formulations.
If your shift schedule is that chaotic (3 nights on, 3 off), it can take a real toll on your internal circadian rhythms. I've known medical residents who use things like light-blocking curtains or full-spectrum (SAD) lamps in their effort to re-set their clocks quickly -- anything that can fool your body temporarily into "day" or "night" mode.
Real valerian root tastes like old dirty socks.
Yeah, lol.
I'd question whether the active compounds in valerian are in high enough concentration in any of these liquids to be effective (or vapeable); we just don't know. Placebo effects can be powerful, though... I just wouldn't rely on an eliquid to help you sleep. There's no data or knowledge on delivery of nonnicotine drugs (and herbs are drugs too) through the PV atomizers.
You can get valerian capsules (don't stick your nose in the bottle!

). They're pretty safe as far as unregulated remedies go; but if you're taking other medications, it's always advisable to ask your doctor before trying any herbal or over-the-counter remedies.
I agree that lower nic is a good idea. (I get bad insomnia if I keep my nic levels at night the same as they were during the day.) The flavors I like in low-nic are different than those I like at higher-nic, so you might find you have to experiment around.