It seems unnecessarily complicated to form a partnership just to solve the problem of not having good records. Having a partnership might involve fees and filing requirements that you'd rather not deal with. And forming a partnership is not going to solve the recordkeeping problem that you are trying to solve. The tax return for the partnership has to allocate the partnership income to each partner. So you would still have to figure out how much each of you contributed, bought, and sold.
I would suggest instead that you do your best to figure out what each of you bought, sold, earned, and now own. File your individual tax returns on that basis. Write it all down in case the IRS questions your numbers. Then split your account into two separate accounts, keep your money separate from now on, and start keeping detailed records.
