My period is 1 week late. Home kit are negative. Fuller breast with mild pains, backache nd mild cramps like my period is coming Shld I do blood test?

Yes. At one week after a missed period, blood test would be positive if you are pregnant and a negative result will out pregnancy. If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD. Practice safe sex.
Yes, "do blood test" The accuracy of a blood betaHCG is greater than that of many "home kits". If you need to know for sure, a blood test may give you a more reliable answer.