"Does my previous earnings affect my current income tax rate."
Short answer: No. Withholding is calculated for each paycheck, and it is calculated as if you made that same rate of pay all year. If you had a job for one week that paid $1000, your employer should withhold an amount that is approximately 1/52 of what your taxes would be if you made $52,000 a year. Even if you had jobs the other 51 weeks of the year with a very different rate of pay, or were unemployed the rest of the year.
Which when you think about it, makes sense. When you get your first paycheck in January, your employer has no way to know for sure what your pay will be for the rest of the year. You might get a much better paying job tomorrow. You might quit and not work the rest of the year. How would he know? Of if you have more than one job during the year, would you want to be required to tell your second employer how much your first employer paid you? You might not mind ... but then again you might not want to. So the reasonable thing to do is to treat each paycheck as if it was "typical". If you get paid once a week, assume your total pay for the year will be 52 times this amount, etc.
Bear in mind that if it's wrong, it doesn't matter in the long run. When you do your taxes the next year, you take your total income and deductions and so forth and calculate how much tax you owe. Then you subtract what was withheld. If too much was withheld, you get a refund. If too little, you have to pay the difference. Unless your withholding is so high that it doesn't leave you enough to live on during the year, or so low that you have to pay penalties, it doesn't matter.