Peat moss by itself really is not good for starting seeds or growing in. Surely you can find something to lighten it up with. I don't know if you have told us where you are located. It would be a big help to change your profile to reflect that. There are hardly any garden questions that can be discussed without regard to location/ climate.
But I looked back and saw that you mentioned a walmart at one point. You know any of the big box stores, you can order on-line pretty much whatever you want and have it shipped to your local store for free and just pick it up from there. I know WalMart.com has perlite, coconut coir, a variety of potting soils, mushroom compost, etc etc. Just order what you want and have it shipped free to your local store.
In the meantime, mixing your peat with crushed lava rock, decomposed granite, coarse sand or whatever you can find would help to improve drainage. Pure peat holds water like crazy, until it starts to dry out and then it sucks water away from your plants and becomes very difficult to wet again.
And your peat by itself is sterile - no nutrients. So you definitely have to be fertilizing your seedlings regularly while they are in sterile medium.