Do I have any chances in obtaining an h1b visa since I'm illegal now and I have bachelor’s degree?

If you are out of status and unlawfully present you cannot get a H-1B within the US. You would have to consular process. However, if you have been out of status and unlawfully present for more than one year, as soon as you leave the US to consular process, you will be barred from reentry for a period of 10 years unless you get a waiver on the basis of extreme hardship to a US citizen spouse.

If you are out of status, you cannot receive any visa. You might be able to obtain legal status through a marriage to a U.S. citizen, regardless of the length of time you would spend in the U.S. before applying. Other possibilities are asylum and cancellation of removal (if your removal would cause an exceptional and extremely unusual hardship to your U.S. spouse, parent, or child). If you do not think either one of these possibilities might work for you, consider leaving the U.S. before your overstay amounts to 180 days and, by doing so, avoiding the penalty of 3-year bar on re-entering the U.S.

You need to see a board certified lawyer like myself. There are too many complications for a brief answer here.