I think you’d better take it to your local bike shop cos adjusting the two little screws is the last thing you should have done.
These screws are there to adjust the position of the derailleur with relation to the cogs when in the top gear and bottom gear…basically to prevent the chain from going into the wheel in the bottom gear, the 25 for example, and to prevent the chain jamming onto the frame in the top gear, the 12 for example. This is normally done once only when you first put on the derailleur…the bike shop would have done this for you.
Now, the fact that the chain skips is easily adjusted by turning the barrel screw at the end of the derailleur where the cable comes out…what this does is loosens or tightens the tension of the chain…
Chain tension is what forces the derailleur to move and to push the chain into each gear, simply put.
One thing you could do though, before you give up and take it to the bike shop is this…
Shift to the small plate, the 39 for example and shift down to the largest cogs, the 12 for example…now check the tension of the cable that comes down the frame…if it is loose it needs to be tightened. Do this by unscrewing the bolt that holds the cable on under the derailleur…get a pair of pliers on one hand to grip the cable and make it tense, by pulling on it…and with your other hand screw in the bolt again to held the cable in place on the derailleur.
Okay, with the hand check the tension of the cable again once you have tightened the bolt.
If its tight then try and change up a gear…if it does not go to the next gear up, say, from a 12 to the 13 cogs turn the barrel screw on the derailleur anti clockwise whilst you turn the pedal with the other hand, until it slips into the next gear…repeat for the other gears…
Turning this barrel screw anti clockwise forces the gear to go to the higher one, from 15 to 16 cogs for example, and turning it clockwise forces it back down a gear…from the 15 to the 14 for example…
Once you have all gears changing as they should without the chain wanting to skip a gear you have finished.
If after all this is still won’t work take it to the bike shop for a quick fix.