Don't worry about your hand hurting. That's actually pretty normal for beginners. With time, your finger-tips will harden so can play for much longer without feeling pain in your left hand. Just make sure you take a break when it starts to hurt. It's no fun playing guitar if you have to endure any amount of pain while playing.
And it's not strictly necessary to get a new guitar just because your fingers hurt. It will, however, help to get the action (distance between the strings and the fretboard) adjusted. I have two of my electric guitars adjusted so they have a very low action, because I find it easier to play faster with a lower action (since there's less pressure needed for fretting the notes).
"Commit yourself to what you love, and things will happen."
- Mika Vandborg, Electric Guitars, "Follow Your Heart"
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Gear:
Chateau PS-10 Cherry Power-Strat
Epiphone G-400 LTD 1966 Faded Worn Cherry
Epiphone Les Paul 100 Ebony (w/ Oil City Pickups Scrapyard Dog PLUS pickups)
Epiphone ES-345 Cherry
Fender 2014 Standard Stratocaster Sunburst
Martin DX1K Acoustic
Fender Mustang II Amplifier
Jet City Amplification JCA22H Tube-head and JCA12S+ cabinet
Pedals...