Is the spacing between Ethernet 10/100 Mbps and USB 2.0 traces critical?
As far as I am aware there is no specific guideline for the separation between Ethernet and USB.  There is however good practices that are employed regarding separating high speed differential traces from any other traces.
Typically the rule would be to keep differential pairs away from other traces by at least 5X the distance to the nearest ground/power plane.
Take for example, 4 layer board that is 1.5mm thick with the following stackup.
LAYER1:  Traces/Components
DIELECTRIC:  14 mils
LAYER2:  Ground
DIELECTRIC:  14 mils
LAYER2:  Power
DIELECTRIC:  14 mils
LAYER4   Traces/Components
A pair of differential traces on layer 1 should be 5 x 14 mils = 70 mils (1.75mm) away from other traces.  Having them further is better.
In your case, you say that the traces are 3.8mm away from each-other.  This would probably be OK in just about any normal stack-up other than a 2 layer board (in which case a 1.5mm board would need 7.5mm separation).