A couple of things - first, take your gross annual income as reported on your taxes and multiply by three. That will be the most you can borrow. Next, they will adjust that based upon your other debts. Finally, that 603 barely qualifies you for a mortgage - they will take a deep dive into your overall credit looking carefully at all your debts and payment history. While you have an outside chance at getting a mortgage, your score will increase the interest rate you will be charged by a percent or more which will lower the amount you can borrow.
You will also be asked to verify that you have at least a 3.5% down payment (no this cannot be borrowed) as well as enough money to cover closing costs plus two months payments - all in the bank when you apply (basically, unless you can get seller assistance on closing costs, you will need 10% of the purchase price in the bank before you apply for the mortgage).
Further, although the FHA calls for at least a 580 credit score, lenders are allowed to set different lower levels and most set those limits at around 640. Hopefully you have had no late payments on any account reported to the credit bureaus in the last 2 years and you have s steady job that you have held for the last two years.