amino acid pka of carboxylic acid
The amino group in $\alpha$-amino acids is electron-withdrawing via the inductive effect. Mesomeric (resonance) effects cannot occur here because there is no conjugation of the nitrogen lone pair with the carboxyl group. There are two equivalent ways of looking at how the EWG affects the acidity:


It stabilises the conjugate base via withdrawal of electron density from the negatively charged oxygens;
It polarises the $\ce{O-H}$ bond further than in the unsubstituted carboxylic acid, making the proton more prone to dissociation.


Therefore, the $\mathrm{p}K_\mathrm{a}$ of glycine is $2.34$, significantly lower than the unsubstituted acid (acetic acid, $\mathrm{p}K_\mathrm{a} = 4.76$). Similar effects are seen in 2-chloroacetic acid ($\mathrm{p}K_\mathrm{a} = 2.86$).



As for the comparison between glycine and 2-chloroacetic acid, one thing to bear in mind is that glycine exists as a zwitterion at neutral pH. Therefore, the relevant acid-base equilibria are:



For $\mathrm{p}K_\mathrm{a1}$, which you are interested in, note that the substituent is no longer merely a $\ce{-NH2}$ group but is now a $\ce{-NH3+}$ group. Despite nitrogen and chlorine having extremely similar Pauling electronegativities, the positively charged nitrogen is now more electron-withdrawing than a simple uncharged chloro substituent.

One could draw some parallels with aromatic chemistry: aniline is rather unreactive (compared to chlorobenzene) in electrophilic substitution under acidic conditions, where it is protonated. Of course, the reactivity of aromatic rings is a kinetic effect whereas $\mathrm{p}K_\mathrm{a}$ is a thermodynamic effect, but the underlying rationale is the same: $\ce{-NH3+}$ is more electron-withdrawing than $\ce{-Cl}$.