I would not test until 4th April, but you could take a test on 29th March. However, if that gives a negative result, you would need to test again on 4th April.
Intercourse does not interfere with the tests themselves. A test will pick up certain hormones in your urine that are there because you have actually become pregnant; implantation has occurred. But it takes several days for the hormones to reach a level that the tests will recognise. After fertilisation (at ovulation - which could be up to 6 days after sexual intercourse), it then takes a few days before implantation. It takes a few more days before a blood test recognises pregnancy, let alone a home test.
If you have taken Emergency Contraception, your cycle will probably have been affected. Although EC may have prevented ovulation, fertilisation or implantation, the next ovulation could come at an unexpected time. Therefore sexual intercourse after taking EC might be at a fertile time in the new cycle. A test result might indicate you are not pregnant from the first sex act but could be too early to detect pregnancy arising from the subsequent act.
When the date of ovulation is unknown or cannot be reasonably assessed, then I would allow 21 days after the last sex act to be able to rely on the result. If an earlier test result is positive, then pregnancy is almost certain. There are not many false-positives.
I think I have responded to all the relevant comments, but there have been many posts, and from different guests. If you still want a response, please ask again.