For the most part, warts look like warts. Zits usually last for a week or two, warts would be around later. Suspect bumps would require a doctor's expertise for a diagnosis.
Thanks for your comments. Still wondering though, are there any symptoms before/as they come? What do they look like at first detection? How can I tell if something is a zit or the beginning of a wart? I feel like even reputable sources on the internet slightly contradict each other.
I would stop worrying now. If you have sex, HPV is unavoidable.
The strains that cause warts are not all that common though. In all probability, your previous partner did not have genital warts, and if he was exposed in 2003, he would have likely cleared the virus long ago.
If you were exposed, warts would usually appear within 2-3 months, but may take as long as 8. Sometimes warts can appear years or decades after exposure, but this is rare.
If you do have warts, deal with them at that time. They are not serious, temporary, and easily treated.
You probably won't get warts, and if you do it is a minor problem, so it is nothing to worry about!