Can a yeast infection and UTI cause a vagina to swell up? And if not, what can and what are treatments?

Yes. A yeast infection can, so can numerrous other conditions - reactions to antibiotics like a UTI med can, tampons, other infections, trauma, allergic reaction, herpes and more. For yeast over the counter vaginal yeast cream, but if it persists or worsens i'd see the doc.
Yes - Rule out BV. Yeast infection causes irritation + can cause vaginal swelling, but best to see a dr, in case of bacterial vaginosis, trichomonas or chlamidia.Also if pregnant or 1st infection.You could self treat if u have had a vaginal yeast infection before.Vaginal cream or suppositories with applicator from pharmacy. Unsweetened yogourt with culture positive or lactobacillus acidophilus good for prophylaxis.