Peppermint or Spearmint?

I have a plant growing but, don't know which it is: peppermint or spearmint? I trimmed it last night and noticed it had long bunches of tiny lavander flowers. Can you help me know what kind it is?

True spearmint, Mentha spicata has long branched, slender inflorescences at the tops of the plant. The leaves are pointy and quite narrow. Peppermint looks more like its Mentha aquatica parent with fairly wide leaves and unbranched, much wider inflorescences. It would be much easier to tell them apart if you had both varieties growing in your garden, because peppermint is much sweeter in scent than spearmint.
An added complication is that there are so many hybrids around that unless you know that you have either one of these two varieties you might have one of the other types that are a mixture of characters and could well look like one but taste like the other. For example, Austrian mint is rather similar to water mint and peppermint in appearance, but has more of a spearmint flavour.
I would suggest that you buy a bunch of fresh spearmint or peppermint in the grocery store and compare the taste to that of your plant. You can then decide how to use your plant.