Yes the filters are required. The STM32 use the analog supply voltage as reference voltage. Thus any noise on the VDDA will end up as noise in your measurement.
As you have low dI/dt, and thus low magnetic fields, this shouldn't be a problem. At least there shouldn't be any significant coupling from the inductor into the STM32. Coupling from the STM32 to the inductor might happen though, but I would guess that the added noise will be swamped by the ADC noise. I would not worry about injecting into the crystal. For one thing, injecting into the crystal (a high Q element) is not easy unless you hit the right frequency. And for another, actually injecting substantial current (or voltage) requires lots of power. As mentioned above, there is not much energy in the fields of the inductors.
What you didn't ask:
You are talking about 1mV signals. The ADC in the STM32 will not be able to resolve that, or rather you will get nothing but ADC noise. 12bit resolution on a 3.3V span mean that 1LSB is 0.8mV. You will need to amplify the signal at least by a factor of 1000 in order to measure anything. Also keep in mind that the STM32 ADCs are known to be very noisy, to the point where ST wrote a few AppNotes how to average ADC samples to have even a chance to get to the advertised resolution. Unfortunately, you cannot filter out all noise. So that ADCs of the STM32 are best described as a GIGO system. (Some of the STM32 ADCs have a measured of ENOB of 6bit!)
DB3 is on the wrong side of UB1. You want to protect the circuit from transients. If the transients pass through the DC/DC converter and destroy
it, you may get the full input voltage on the 3.3V rail, which in turn will fry your ciruitry (DB3 will not protect against that, either because it doesn't conduct or because it will be fried and potentially form an open circuit).
There is a too big value gap between CB1 and CB2. The resonance of CB2 (acting as a capacitor) and CB1 (acting as an inductor) might cause EMI. Either add at least a 33nF capacitor or better, a 10nF and a 100nF. CB3 can be IMHO left out, as the module's on module capacitors will already block those high frequencies. Alternatively, you can choose one of the Murata EMIFIL pass through capacitors, which have a much higher self-resonance frequency, thus can replace a few smaller valued capacitor steps.
LB2 will potentially induce EMI problems, unless you know very well how to design your ground paths. It's best to leave it out and filter on the power rail only.
You do want to add at least 1nF, 10nF 100nF capacitors between UB1 and LB1. Otherwise the short wire to LB1 and the stray capacitance of LB1 will cause EMI problems.
LB1 (together with LB2 if not removed) and CB4 form a resonant circuit. Unless it's resonance frequency is way out of everything that you produce (very unlikely) you will get resonance effects (as John D mentioned in the comments above). You should add a properly sized R-C snubber circuit to dampen this resonance.