The itching, redness and swelling right after intercourse, with no odour or discharge, usually points to skin irritation from friction, semen or a product used around that time, rather than a yeast infection. But the burning on urination, strong smelling urine and that feeling of incomplete emptying do suggest a urinary tract infection alongside it.
Next Steps
Get a urine routine and culture test done soon to confirm the UTI and guide treatment. Wash the area with plain water only, and avoid scented soaps or wipes until the irritation settles.
Health Tips
See a gynaecologist or physician if the swelling increases, you develop fever, or it doesn't ease within two to three days.