It is a mistake many people make. Don't chastise yourself too harshly. I am an indifferent typist myself, but I have the luxury of Microsoft "Word" if I remember to use it, I can compose messages in it, then select all, copy and paste in the GenForum box. Once in a while the spell checker lets me type "doe snot" instead of "does not", so people think I'm talking about a lady deer with a runny nose, but it is pretty good about capitalization and punctuation. It helps me spell uncommon words, like "chastise", too.
Without knowing for sure if the man on your birth certificate is your father, you are stuck on that line. If one of your aunts, uncles or cousins would be willing to do a DNA test you could be sure he either was or wasn't, but they are expensive. If he would be willing it would be much easier, but it sounds like he isn't.
There is a lot of genealogy data available for free on the Internet, most of it accurate. "Most" is the operative word here, and figuring out which bits are accurate is hard. Most of the data concerns people who died before 1920, too. You may be able to find your mother or her parents on
If you do, the Social Security Administration will sell you a copy of an SSN application for $27. It is better than a death certificate because the person himself / herself filled it out while he/she was still living. SSN applications have the person's name, birth date and birth place; mother's maiden name, father's name; place of employment, job title and home address at the time of application.
Click on "SS-5" on the SSDI site and the wizards at Roots Web will even format a letter to the SSA for you.