The safe answer is it depends, but let's look at it closely.
Typically, frontend amplifiers have a maximum input power (safety/breakdown rating) of about 20dBm. You transmitted at 38.5dBm at a distance less than one meter. You most likely exceeded that 20dBm line, unless you removed the antenna from the receiving HT.
Precise link loss calculation is rather meaningless because of close proximity (the antennas are in each other's reactive near fields) and there probably are a lot of reflections in your environment.
However, I don't know your HT's frontend amplifier circuit/device, and it may have a much more robust device. Also, safety ratings have some margins built in. So, I think it is somewhat unlikely that permanent damage was made.
Some frontend preamps are very robust. Some circuits (like dual J310 common-gate amp... though I don't think such an amp was ever used in an HT) were known to take 10W and still not break. So, the answer really is it depends.
EDIT/ADD
I just downloaded the service manual for Yaesu VX-6R. The frontend amplifier for 2m is 2SC5555, a bipolar transistor. I think it is most likely ok/undamaged. The most obvious sign of permanent damage is lack of receiver sensitivity, making it unable to receive weak stations it was able to pre-damage. A bit more subtle damage is increased internal noise, also making it harder to receive weak signals.