This ^^^. Please do not be paranoid about punctures or getting stranded. The risk is low but the hazard (consequence) nevertheless needs mitigating. Do so by becoming sufficiently competent, through videos and then practice. Not that much difference from your studies; but 'hands on'. I have a daughter who like you has just started at uni. She has taken her bike and before term started I 'forced' her to take a wheel off, remove the tyre, replace the inner tube and refit the tyre, pump up and refit the wheel (and readjust brake). You are carrying what you need (no need to repair: just replace tube). Pump the tyre up with your 'mini-pump': when you cannot depress your thumb into the tyre that's well hard (enough) to support your light weight. I have suggested appropriate pressures for your tyres in an earlier thread.
Competence breeds confidence.