The condom broke while I had sex on my period. I took emergency contraception the next morning. My period seemed to have ended until I had protected sex the following day where I bled heavily. It got better in a week. Now, four weeks later, my period is a few days late.

It is likely your period is just off a bit. A few days either side is not unusual. Give it several more days and see what happens. Odds are you are not pregnant, as emergency contraceptives tend to work quite well, but of course no contraceptive will be 100% every time.

Two months ago my cycle was 28 days, last month it was 35.. Now I am beyond 35 days, 38 to be exact. Any other reason why?

Since you are posting in the child & teen health section I am guessing you are in your teens. Having irregular cycles for a few years during the teen years is not unusual so it could just be that. Having sex around the time of your period can cause you to bleed a bit more as well.

Cycles can be thrown off due to illness, stress, significant weight changes, hormone fluctuations, infection, etc.. Once in awhile it just happens for no apparent reason. You might even skip a period now and then. Some doctors don't even do blood tests until two periods have been missed in a row due to it not being uncommon.