If you still have the links to the deleted posts, you may be able to edit them and then flag for moderator attention. If not, then a moderator on MSO may be able to pull the deleted answers for you, assuming you do intend to make the necessary improvements.
Improving them and getting upvotes would lift the ban.
Additionally, the link you got with the ban should explain other techniques for lifting the ban, which is automated and can only be lifted by performing positive actions on the site, such as editing, asking well-researched questions (assuming you're only answer-banned), etc.
For instance, you can suggest edits to other posts that need improvement. If those edits are improved, that will give you rep and help undo the ban.
If you've edited the deleted posts to add in your affiliation, you can still flag them, as long as you have a link. Or flag the question and explain the situation.
In the future, just be careful. If your goal here is to promote a project you're working on, Stack Overflow might not be the right site for you. If an occasional post contains your product, that's fine, but if all your answers contain links to your product, you're here for the wrong reason. ;)
Please see the FAQ section on Promoting for more details:
May I promote products or websites I am affiliated with here?
Be careful, because the community frowns on overt self-promotion and tends to vote it down and flag it as spam. Post good, relevant answers, and if some (but not all) happen to be about your product or website, so be it. However, you must disclose your affiliation in your answers.
If a huge percentage of your posts include a mention of your product or website, you're probably here for the wrong reasons. Our advertising rates are quite reasonable; contact our ad sales team for details. We also offer free community promotion ads for open source projects and non-profit organizations.
Hope this helps!