Can you not just wear a cycling cap? or if your head gets too hot the equivalent but a visor? Saves buying a new helmet.
that looks like a terrible helmet..
https://www.evanscycles.com/giro-reverb-helmet-EV191246
have used the one above for a year-ish and it's pretty good.
a bad fitting helmet is probably worse than no helmet I'd say go to a bigger bike shop and try a few on, if you want to get something cheaper go to decathlon or halfords(I got my boardman helmet from them)
or even evanscycles
Cycle cap under helmet for the win. Looks pro as well.