Can I breastfeed even if my boobs are really big?

Yes. If you are having difficulty with breast feeding, definitely consult a lactation specialist before you give up! a change in position may be all that is required for your baby to have a good latch. Some mothers who have had breast reductions may find it difficulty to breast feed, however large breast size should not be problematic.
Yes. Find a good position for yourself and and the baby and find which angle works best. Good breast hygiene is most important. A comfortable nursing bra can also work wonders.