Altogether, digital thermometers are known to be very inaccurate.2. If you want the most accurate reading, a fever should be measured rectally, not axillary (in the armpit)1.
So therefore, different limits apply to axillary temperature measurements:
In patients older than 1 month, the mean difference (SD) between the
rectal and axillary temperatures was 1.04°C (0.45°C); thus, the
axillary temperature was adjusted by adding 1°C, and no adjusted
axillary temperature differed from the rectal temperature by more than
Comparison of Rectal, Axillary, and Forehead Temperatures, Arch Pediatr Adolesc Med
The basal body temperature varies from 36.5 up to 37.5 degrees celsius according to Elsevier, 20173. Studies from 2008 allow values of <= 38.3 degrees.4.In your case, your first reading was 37.7 basal temperature (not really sick), and the second 38.0 (maybe slightly sick).
Both values aren't accurate for medical differential diagnosis (axillary measurements, and varying quite a lot), but body temperature really doesn't tell you a lot anyway. If you feel sick, consider yourself sick. I personally probably have above 37 degrees axillary in the morning after a cozy sleep, and unless I feel sick, I wouldn't consider myself sick if my temperature is 0.3 above guidelines and I lack other symptoms of any sickness.
1: S. T. ZengeyaI. Blumenthal, Modern electronic and chemical thermometers used in the axilla are inaccurate, European Journal of Pediatrics
2: An investigation into the accuracy of different types of thermometers, Nursing Times
3: Luxem, Jürgen; Runggaldier, Klaus: Rettungsdienst RS/RH, Elsevier. 2017. German book for the paramedic education
4: Laupland, B. Fever in the critically ill medical patient., 2008.
Temperature Measurement for Patients with Fever, US Pharmacists, 2008.