This might get closed as off topic, it's a bit subjective as to whether this is a "go see a doctor" type of response. But as a guy who's been deadlifting for a while, I'd offer up this feedback. This is based in my own personal experiences and discussion with my doctor.
- My doctor hates deadlifts because she has several patients a week coming in with back injuries from them. She's amazed that I (and really anyone) is capable of deadlifting big weights for years on end without problem.
- My initial problem with deadlifting was that I started mix-and-matching my cleans form in. With cleans, you want your butt a bit lower because you need a lot of leg spring. With bigger weights (the kind that you deadlift, the kind you can't clean), you really want to have a neutral spinal position.
I suffered a herniated disc, complete with sciatica, several years ago because the form that I thought was good was actually bad (butt too low, spine hyperextended).
With a spinal injury like that, the pain is amazingly fast and pronounced. It's not dull: it's fast-car-accident pain that literally puts you on the floor. You wouldn't be able to tie your shoes, get up from a chair without major effort, etc.
It sounds more like you have a muscle strain (pulled muscle). The good news is that that will heal quicker, usually in the form of days instead of weeks.
You'll want to wait for the pain to become "dull", then ramp up your lifting stopping well clear of "ouch" pain. Another thing to consider is that muscle pain can often cause your form to suffer, as you favor muscles that don't hurt which can in turn load you up in bad ways. So if it hurts in a bad way (good vs bad pain), stop immediately: you will go backwards.
In my own experience, the following three items really helped me to deadlift better and not feel it in my lower back.
Consider doing ab and glute exercises specifically, as isolated assistance exercises in this department make it easier to concentrate on engaging them in compound lifts.