I want to get pregnant. Can I?
I am 23 and newly married. I had my last menstrual period on 18 June. My periods take 26-29 days long. I had sex on 28 June and 1 July which were regarded to be in the fertile period. Later I felt fatigue, mild nausea, bloating and mild leg ache on 8-12 July and sharp abdominal pain for two nights. I know these are the signs for next menstrual period but I've never felt like these. So, I made home pregnancy test but the result was negative. I've had my breast pain on 13 July and nipples getting darker but the previous symptoms seems to be milder. For sure, I made home pregnancy test again on this morning,15 July, but the result was negative again. But I just feel I am pregnant.

You are testing too soon. If you miss your period, wait 2 weeks then test with the first urine of the morning.

It is very possible you are getting false negatives because you are testing too soon. You need to wait until your period is two weeks late before testing. When you DO test, make sure to use first morning urine.

You are doing everything wrong, except the part of having sex.

First no, unless you are tracking basal temp you have no idea of your fertile times, I am assuming you are looking at some silly online or phone app. They are worthless since all women do not ovulate on specific days between periods.
So if you want to get pregnant, you need to start tracking that.

Next you know the sperm takes about 3 days to reach the egg.

Also there are almost no signs in most women, before a missed period and often into the next month.

You can not test till you are at least two weeks late for your next period, then only test with first urine of morning