When is it okay for me to start working out again after a pretty serious uti?

Soon as able to. One can perform their normal daily routine and activities while on treatment for a UTI except possibly for sexual activity as long as the symptoms are not too bothersome.
Any time gradually. Work out is not a risk for causing uti. So, the general condition is the main factor to worry about here. Do what you can do without pushing youself much until you are back to your normal baseline of strength.
When you feel well. Should be ok to return to work when you are no longer symptomatic and you feel up to working out. Probably at least 2 weeks if your kidneys were involved, much less if UTI confined to your bladder.