You won't notice much difference. 28 vs 37 tyres will give you about 10-20 seconds faster time per kilometre up hill I think, but you will not FEEL like you're going any easier, or faster. If you get tired, get lower gears (if your knees hurt from too low cadence-high muscle effort), or a lot lighter race bike (if you don't have a lot of stuff to carry and aren't fat ).

Clipless pedals might also help. Shimano MTB SPD stlyle, with appropriate shoes.