"I have only BEEN WORKING for a month" ------> 我才刚刚工作一个月
From the day I started my job, up to now I have been working for a month and I will continue working here.
In Chinese, it's hard to translate the structure "have been doing". So from the sentence ”我才（刚刚）工作一个月“，you can't get it whether he will continue working or not. And this exactly could be understood as "I only worded for a month, (and then I was fired)."
"I only WORKED for a month"--------》我只上了一个月的班
The structure with "了" N ”过“
The main differences can be roughly divided into two parts, the structure and the meaning.
About the structure:
1.in a negative sentence with "没XX",：
【没X了】，we ignore the "了"，we say 【没x】
while 【没X过】，we still say 【没X过】
eg. 去过北京[He has been to Beijing]。 (否定形式：没去过北京。He hasn't been to Beijing)
去了北京[He went to Beijing.]。 (否定形式：没去北京。He didn't go to Beijing, maybe go to Shanghai, Hong Kong....)
2. we have 【verb+了+verb】 but we don't have 【verb+过+verb】
eg. 看了看 = have a look (at sth) / 尝了尝= taste sth.
他看了看他的手表，告诉她现在是12点=He took a look at his watch and told her it was 12.
wrong to say X [看过看] X
ABOUT THE MEANING:
1.【verb+ 过】usually refers to a happened event,
Last year when I went to Beijing, I paid a visit to the Forbidden City.
When I was studying in Beijing, I ate the roast duck with some friends.