Personally I LOVED my portacath. I had to do chemo twice as I had a recurrence. I, like you didn't have it for first 6 chemos. However the drugs absolutely trashed my veins and they still to this day haven't recovered. Luckily as I didn't have chemo in my hands the veins there are ok, but painful. It is still a challenge when I need an IV or blood tests. The portacath, whilst an ugly little bump, and yes it has left a little scar, but the ease with which the next chemos went in after the recurrence was amazing. The nurses also used it if I had some blood tests due at the time of chemo. If they are having trouble with your veins now, they probably aren't going to get better. The other arm is not a great idea due to the lymphedema risk(I have that also).
If you really don't want the port then you could try really well hydrating yourself before your infusion. Start the day before and drink heaps and lots before the infusion. Also go dressed in warm clothes as your veins hate the cold as the vasoconstrict and go into hiding. I know veins as I am a nurse at the blood bank ;). That's your best shot. It may work, but if it doesn't the port really makes infusions a breeze.
Hugs.
Paula xxxx