Because I help out at a health center, I was told quite a long time ago that I would get priority in receiving a vaccination if there are any cancellations from the general public. However, my turn has not come yet.
ご質問ありがとうございます。
"Because I help out at a health center"＝「保健所で手伝っているので」
"I was told quite a long time ago that"＝「私はかなり前に～と言われた」
"I would get priority in receiving a vaccination"＝「ワクチン接種を優先される」
"if there are any cancellations from the general public."＝「一般の人達からのキャンセルがあった場合」
"However, my turn has not come yet."＝「しかし、私の順番はまだ来ていない。」
ご参考に。
I was told I could get leftover vaccines on a priority basis.
「ワクチンの余りを優先的に接種出来る」という表現は、"I was told I could get leftover vaccines on a priority basis." になります。
"I was told" は「～と聞きました」と述べています。
"leftover vaccines" は「余ったワクチン」を意味します。
"on a priority basis" は「優先的に」を示し、他の人よりも優先されることを指します。
アメリカ合衆国 
