Could an entertainment attorney help me with my songwriting career?

You can hire an attorney anywhere, U.S. or overseas, to help you with this.

A good music attorney could certainly read the contracts, look at the publisher, and explain things to you. Most likely, your songs should be registered for copyright with the U.S. Copyright Office and you should name a publisher and join a PRO. Then whatever international use of the songs you may wish to work out with this publisher or with others, that is icing on the cake, if the contract is right for your needs. As to a masters use license, this pertains to a particular recording and would be worked out with your record label, if you have one, or with you, pertaining to a particular use of a particular recording of a song by a particular party for a particular purpose. A good music lawyer should know about these things and should be able to explain them all to you. She will also be able to read the contract being offered or write a suitable contract. If you have songs that are being recorded by others overseas, you may need to belong to an international PRO or to international publishing administrator.

Yes - you should consult with an entertainment lawyer before signing ANY contracts regarding your songs. GOOD LUCK!

Given the things you said, I think it is better to work with a single attorney who knows you well and will do a good job for you. Consider looking for another attorney if you are not satisfied with the one you are now working with.