First, congratulations on the engagement, and also giving a very good download of your condition, you seems to be well aware of what all information is needed to seek a good medical advice, except one. How long is your period?? That is from one cycle's 1st day of bleeding to the next cycle of 1st day of bleeding.
2nd, you seem to miss the point of "emergency" contraceptive pills. You mustn't use them regularly. As the name say they are only for emergency. And yes, they do have side-effects, and may cause complications if used regularly. Try to avoid them if you can.
LMP was on 29th, I am assuming that's the day your bleeding started, lasting for 2-3 days. In that case your cycle started on 29th May. Assuming that you have 28 days cycle (you haven't written length) your next period should start on 25th June, naturally on an average. Now, given that you have taken emergency contraceptive pills, twice, they might delay the periods by few days.
How to plan for unprotected sex? There are several apps that help you record your periods, and tell you ovulation n fertility windows. But do consult a gynaecologist to understand how to best plan for it, and the probabilities of pregnancy in a low fertility window. You need to understand your ovulation cycle well, and even if you calculate everything right, there still is a slight chance that you get
pregnant, however small that chance is. Best to be on normal oral contraceptive pills (OCPs). For their effect n doses, consult a gynaecologist. Modern OCPs are quite safe, and have little or no side effects. However, no prescription should be taken without consulting a doctor in person.
In your case there is a very little chance to get pregnant, however, do take UPT few days after your missed period (lets say on 30th), if you don't get your periods till then. Right way of taking UPT is using the first urine in the morning. And if the bleeding still doesn't happen, to be sure, you should repeat the test in few days again. If you still don't get bleeding, and the
pregnancy test is negetive both time, You must consult a gynaecologist.
And do understand the fact that in the field of medicines every thing is probabilistic. Hence for any abnormalities, consulting a medical professional, is must.
Hope you get your periods soon. Have a healthy menstruation.